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30351.

The half life of the homogeneousgaseous reaction SO_2Cl_2rarrSO_2+Cl_2 which obeys first order kinetics is 8.0 minutes. How long will it take for the concentration of SO_2Cl_2 to the reduced to 1% of the initial value ?

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Solution :We KNOW that , k = `0.693//t_(1//2)`
k = 0.693/8.0 `=0.087 "MINUTES"^(-1)`
For a first order REACTION
`t=(2.303)/klog.([A_0])/([A])`
`t = (2.303)/(0.087"min"^(-1))LOG.(100/1)`
t = 52.93 min
30352.

The half-life of Tc^(99) is 6.0 hr. The delivery of a sample of Tc^(99) from the reactor to the nuclear medicine lab of a certain hospital takes 3.0 hr. What is the minimum amount of Tc^(99) that must be shipped in order for the lab to receive 10.0 mg?

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20.0 mg
15.0 mg
14.1 mg
12.5 mg

Answer :B
30353.

The half-life of radium (226) is 1620 years. The time taken to convert 10 grams of radium to 1.25 grams is

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810 years
1620 years
3240 years
4860 years

Solution :`t = (2.303 XX t_(1//2))/(0.693) "LOG" (N_(0))/(N)`
30354.

The half-life of Rn is 46 days, what amount will be left from 2 mole of it after 138 days?

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`0.25` mole
`1.25` mole
`0.40` mole
`0.62` mole

Solution :Number of half lives gone = `(138)/(46) = 3`
`N_0 = 2` mole, `N_t = ?`
As, `N_t = N_0 xx (1/2)^(n) implies N_t= 2 xx (1/2)^(3) = 2/8 = 0.25` mole.
HENCE 0.25 mole of .Rn. will be LEFT from 2 mole of it after 138 days.
30355.

The half-life of radioactive sodium is 15.0 hours. How many hours would it taken for 64 gms of sodium to decay one-eighth of its original value

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3
15
30
45

Solution :`:' 2.303 "log" (No)/(N) = LAMDA t`
and `lamda = (0.693)/(t_(1//2)) = (0.693)/(15)`
or `lamda = 0.0462`
`:.` using equation (i) we GET
`2.303 "log" (64)/(8) = 0.0462 xx t`
or `t = 45`hr
30356.

The half life of radioactive sodium is 15 hours its disintegration constant is

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`0.0462 h^(-1)`
`0.0642 h^(-1)`
`0.0462 s^(-1)`
`0.0462 "min"^(-1)`

SOLUTION :`K = (0.693)/(t_(1//2)) = (0.693)/(15) = 0.0462 hr^(-1)`.
30357.

The half life of radioactive sodium is 15 hours. How many hours would it take for 64 g of sodium to decay to one-eight of its original value?

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3 HOURS
15 hours
30 hours
45 hours

SOLUTION :d) `t=2.303/k log (No)/(NT)`
`t=(2.303 xx(15 "hours"))/(0.693)log64/8`
`=(2.303 xx 15 xx 0.9030)/(0.693) = 45` hours
30358.

The half life of radioactive element depends upon the

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NATURE of element
Temperature
Pressure
Amount of the element

Answer :A
30359.

The half life of paracetamol with in the body is ....

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2 HOURS
2.5 hours
6 hours
10 hours

Answer :B
30360.

The half-life of cobalt - 60 is 5.26 years. Calculate the % activity remaining after 4 years.

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SOLUTION :`t^(1//2)=5.26 years`
t=4 years
here to findthe % of activity (i.e) to find`(N)/(N_(0))`
`log(N_(0))/(N)=(lambdaxxt)/(2.303)`
`=(0.693)/(5.26)xx(4)/(2.303)`
=0.2288
`(N_(0))/(N)` = ANTILOG (0.2288)
=1.693
% of activity = `0.59 XX100`
=59%
30361.

The half-life of C^(14 is 5760 years.for a 200 mg sample ofC^(14) , the time taken to change to 25 mg is

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11520 years
23040 years
5760 years
17280 years.

Solution :`R_(0) = 200 mg , R= 25 mg , R = 25 mg , t_(1//2) = 5720` years
SUPPOSE REQUIRED years are x.
ALSO, suppose no. of half lives = n
`:. (R/(R_0))= (1/2)^n IMPLIES (25/100) = (1/2)^(n)`
`implies (1/8) = (1/2)^(n) implies (1/2)^(3) = (1/2)^(n) implies n = 3`
`:. n = x/(5760) implies 3 = x/(5760) implies x = 5760 xx 3 = 17280` years.
30362.

The half-life of Co^(60) is 7 years. If one g of it decays, the amount of the substance remaining after 28 years is

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0.25 G
0.125 g
0.0625 g
0.50 g

Solution :`n = (28)/(7) = 4, N = (N_(0))/(2^(n)), N = (1)/(2^(4)) = (1)/(16) = 0.0625 g`
30363.

The half life of a substance in a certain enzyme-catalysed reaction is 138 s . The time required for the concentration of the substance to fall from 1.28 mg L^(-1) to 0.04 mg L^(-1) is

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690s
276 s
414 s
552s

Solution :Enzyme catalysed reactions are initially FOLLOW FIRST ORDER kinetics when concentration decreases `1.28mg l^(-1)` to 0.04 mg `l^(-1)` . Then five half-life completed
No. of half-lives =5
So , TIMES required = `5 XX 138 = 690 `s
30364.

The half-life of a substance in a certain enzyme-catalysed reaction is 138 s. The time required for the concentration of the substance to fall from 1.28" mg L"^(-1)" to "0.04" mg L"^(-1), is

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414 s
552 s
690 s
276 s

Solution :AMOUNT LEFT after n HALF lives `=([A]_(0))/(2^(n))`
`0.04 = (1.28)/(2^(n)) or 2^(n) = 32 = 2^(5) therefore n = 5`
Time taken ` = 5 ` half lives`= 5 xx 138 s = 690 s.`
30365.

The half life of a reaction is inversely proportionaly to the square of the initial concentration of the reactant . Then the order of the reaction is :

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0
1
2
3

Solution :(D) `t_(1//2) prop [A]_(0)^(1-N)`
where n = ORDER of reaction
SINCE `t_(1//2)prop (1)/([A_(0)]^(2))`
`implies t_(1//2)prop[A_(0)]^(-2)`
`1-n =-2 ` n=3.
30366.

The half-life of a reaction is halved as the initial concentration of the reactant is doubled. The order of reaction is

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`0.5`
1
2
0

Solution :`t_(1//2) PROP (1)/([A_(0)]^(n-1)), ((t_(1//2))1)/((t_(1//2))2) = ([A_(0)]_(2)^(n-1))/([A_(0)]_(1)^(n-1)) = {([A_(0)]_(2))/([A_(0)]_(1))}^(n-1)`
`(t)/(t//2) = (2a)/(a)^(n-1) or 2 = (2)^(n-1)`
or ` n -1 = 1 or n =2 `
30367.

The half-life of a radionuclide is 69.3 minutes. What is its average life (in minutes)

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100
`10^(-2)`
`(69.3)^(-1)`
`0.693 xx 69.3`

Solution :Average life
`(TAU) 1.44 t_(1//2) = 1.44 xx 69.3 = 99.7 ~~ 100` MINUTES
30368.

The half-life of a radioisotope is four hour. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

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3.125 G
2.084 g
1.042 g
4.167 g

Solution :`(N)/(N_(0)) = ((1)/(2))^((T)/(t_(1//2))), (N)/(200)= ((1)/(2))^((24)/(4)), (N)/(200) = ((1)/(2))^(6)`
`N = (200)/(64) = 3.125 g`
30369.

The half-life of a radioisotope is 20 years. If the sample has an initial activity of 640 dps,than what will be its activity after 80 years?

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20 dps
30 dps
40 dps
50 dps

Solution :`t_(1//2) = 20 "years" , t = 80` years,
`N_0 = 640 dps, N_t = ?`
Number of half lives gone `(n) = (80/20)= 4`
Now, `N_t = N_0 XX (1/2)^(n) = 640 xx (1/2)^(4) = (640)/(16) = 40 dps`
The ACTIVITY of the radioisotope will be 40 dps after 80 years.
30370.

The half life of a radioisotope is 4 hr. If the initial mass of the isotope was 200 g, the mass remaining after 24 hr undecayed is:

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3.125 g
2.084 g
1.042 g
4.167 g

Solution :No. of half life periods =6
Mass left `=([A]_(0))/(2^(6))=(200)/(2^(6))`
`=(200)/(64)=3.125g`
30371.

The half-life of a radioactive nucleide 'X is 24 hours, the time required for 12.5% of the original X to remain is :

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1 days
2 days
3 days
4 days

Answer :C
30372.

The half - lifeof a radioactive isotope is three hours. If the initial mass of the isotope was 300 g. the masswhichremainsundecayed in 18 hourswould be

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2.34 g
1.17 g
9.36 g
4.68 g

SOLUTION :NUMBER of half -lives(N) =` ("Total time")/( t_(1//2)) = 18/3 = 6`
` N = N_(0)/(2^(n)) = 300/2^(6)4.68 g`
30373.

The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256g, the mass of it remaining undecayed after 18 hours would be

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`4.0 G`
`8.0 g`
`12.0 g`
`16.0 g`

Solution :`N_(t) = N_(0) ((1)/(2))^(N) , N_(t) = 256 ((1)/(2))^(18//3) = 256 ((1)/(2))^(6) = 4`
30374.

The half-life of a radioactive isotope is 3 hours. Value of its disintegration constant is

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0.231 PER HR
2.31 per hr
0.2079 per hr
2.079 per hr

Solution :`K = (0.693)/(t_(1//2)) = (0693)/(3HR) = 0.231` per hr.
30375.

The half life of a radioactive isotope is three hours. If the initial mass of the isotope was 300 g, the mass which remained undecayed in 18 hours would be :

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2.34g
1.17 g
9.36 g
4.68 g

Solution :AMOUNT LEFT after N HALF lives `=(N_(0))/(2^(n))=(300)/(2^(6))`
`=(300)/(64)=4.68g`
30376.

The half life of a radioactive isotope is 2.5 hour . The mass of it that remains undecayed after 10 hour is (If the mass of the isotope was 16 g) :

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32 g
16 g
4 g
1 g

SOLUTION :
30377.

The half-life of a radioactive isotope is 1.5 hours. The mass of it that remains undecayed after 6hours is (if the initial mass of the isotope was 32g)

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32g
16g
4g
2g

Answer :D
30378.

The half-life of a radioactive element is 6 months. The time taken to reduce its original concentration to its 1.16 value is

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1 years
16 years
2 years
8 years

Solution :`t = (2.303 XX t_(1//2))/(0.693) "log" (N_(0))/(N), N = (1)/(16)`
30379.

The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample ?

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`45.6 XX 10^(23)` atoms
`4.56 xx 10^(23)` atoms
`4.56 xx 10^(24)` atoms
`4.56 xx 10^(25)` atoms

SOLUTION :`N_t = N_0 (1/2)^(n)`
`n = 4//10`
`:. N_t = 6.022 xx 10^(23) xx (1/2)^(0.4) = 4.56 xx 10^(23)`
30380.

The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample

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`45.6 XX 10^(23)` ATOMS
`4.56 xx 10^(23)` atoms
`4.56 xx 10^(24)` atoms
`4.56 xx 10^(25)` atoms

Solution :`N_(t) = N_(0) ((1)/(2))^(n) n = 4//10`
`:. N_(t) = 6.022 xx 10^(23) xx ((1)/(2))^(-.4) = 4.56 xx 10^(23)`
30381.

The half-life of a radioactive element is 100 minutes . The time interval between the stages 50% and 87.5 % decay will be x xx 40 min . The value ofx is _____

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SOLUTION :`100 overset(100)(to) 50 overset(100)(to) 25 overset(100)(to) 12.5 , t = 2 xx 100 = 200` MM
30382.

The half life of a first order reaction x rarr products is 6.932 xx10^4 s at 500 K . What percentage of x would be decomposed on heating at 500 K for 100 min . (e^(0.06)=1.06)

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Solution :Given `t_(1//2) = 0.6932xx10^4s`
To solve : when t = 100 min , `([A_0]-[A])/([A_0])xx100= ? `
We known that a first order reaction , `t_(1//2)=(0.6932)/K`
`k=(0.6932)/(6.932xx10^4)impliesk=10^(-5)s^(-1)`
`k=(1/t)LN(([A_0])/([A]))`
`10^(-5)s^(-1)xx100xx60s=ln([A_0])/([A])`
`0.06=ln(([A_0])/([A]))`
`([A_0])/([A])=E^(0.06)=1.06`
`:. ([A_0]-[A])/([A_0])xx100%=(1-([A])/([A_0]))xx100%=(1-1/(1.06))xx100%=5.6%`
30383.

The half -life of a first order reaction [k=(2.303)/(t)"log"((a)/(a-x))] is

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DIRECTLY proportional to a
inversely proportional to 'a'
independent
proportional to (a - x)

SOLUTION :It is a FACT .
30384.

The half- lifeof a firstorderreactionis 900min at820 k Estimateits half- lifeat 720 kif theenergyof activationof thereactionis 250kJ "mol"^(-1) (1.464 xx10^(5)min)

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Solution :HINT `: (k_(2))/(k_(1))= ((t_(1//2))_(1))/(t_(1//2))_(2)`
Half- LIFE period`-1.46xx 10^(5) min`
30385.

The half-life of a first order reaction [k=2.303/t log (a/(a-x))] is

Answer»

directly proportional to 'a'
inversely proportional to 'a'
independent of 'a'
proportional to (a - x)

SOLUTION :For a first order reaction
`k = (2.303)/(t) "LOG" (a)/(a-x) ` , when `t = t_(1//2) , x= (a)/(2)`
`therefore t_(1//2)= (2.303)/(k) "log" (a)/(a- (a//2))`
or `t_(1//2) = (2.303)/(k) "log" 2 = (2.303 xx 0.3010)/(k) = (0.693)/(k)`
i.e., Half LIFE of a1 order reaction is independent of INITIAL concentration 'a' of reactant.
30386.

The half life of a first order reaction is 69.35 sec . The value of the rate constant of the reaction is

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`1. 0 s^(-1)`
`0.1 s^(-1)`
`0.01 s^(-1)`
`0.001 s^(-1)`

SOLUTION :`K = (0.693)/(t_(1//2)) = (0.693)/(69.35) = 9.99 xx 10^(-3) = 0.01 s^(-1)` .
30387.

The half- life of afirstorderreactionis 1.7hours. Howlongwill it takefor 20%of thereactanttodisappear ?

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SOLUTION :Timerequiredfor 20%reaction=32 .86 MIN
30388.

The half-life of a first order reaction is 30 min and the initial concentration of the reactant is 0.1 M. If the initial concentration of reactant is doubled, then the half-life of the reaction will be

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1800 s
60 min
15 min
900 s

Answer :A
30389.

The half life of a first order reaction is

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INDEPENDENT of the initial CONCENTRATION of the reactant
directly PROPORTIONAL to the initial concentration of the reactant
inversely proportional to the initial concentration of the reactant
directly proportional to the square of the initial concentration of the reactant.

ANSWER :A
30390.

Thehalf life of a firstorderreactionis 30 minand theinitialconcentrationof thereactant is 0.1M . Ifthe initialconcentrationofreactantisdoubled,thenthehalflife ofthe reactionwill be

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1800S
60 min
15 min
900s

Answer :A
30391.

The half life of a first order reaction is 100 seconds. What is the time required for 90% completion of the reaction?

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100 sec.
200 sec.
333 sec.
500 sec.

Answer :C
30392.

The half life of a first order reaction is 100 seconds at 280 K. If the temperature coefficient is 3.0 its rate constant at 290 K in s^(-1) is

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`2.08xx10^(-3)`
`2.08xx10^(-2)`
`6.93xx10^(-3)`
`6.93xx10^(-2)`

ANSWER :B
30393.

The half life of a first order reaction is 10 minutes. If initial amount is 0.08 mole/litre and concentration at some instant ‘t’ is 0.01 mol/litre, then the value of ‘t’ is :

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10 MINUTES
30 minutes
20 minutes
40 minutes

Solution :0.08 MOL `l^(-1)` to `0.01` mol `l^(-1)` involves 3 half-life . So the t is 30 minutes .
30394.

The half-life of a first order reaction is 10 minutes. If initial amount is 0.08 mol/L and concentration at some instant is 0.01 mol/L, then t is

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10 minutes
30 minutes
20 minutes
40 minutes.

Solution :`K=(0.693)/(t_(1//2))=(0.693)/(10)`
`t=(2.303)/(k)"LOG"(0.08)/(0.01)=(2.303xx10)/(0.693)log` 8=30 minutes
30395.

The half-life of a first order reactionhaving rate constant K = 1.7 xx 10^(-5) s^(-1) is

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12.1 H
9.7 h
11.3 h
1.8 h

Solution :k = `1.7 xx 10^(-5) s^(-1)`
`t_(1//2) = (0.693)/(k) = (0.693)/(1.7) xx 10^(5) = 11.32` h.
30396.

The half life of a first order reaction AtoB+C is 10 minutes. The concentration of 'A' would be reduced to 10% of the original concentration in

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10 minutes
33 minutes
90 minutes
70 minutes

Answer :B
30397.

The half life of a 1^(st) order reaction is 1 min 40 seconds. Calculate its rate constant (k)

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`k=6.9xx10^(-3) "MIN" ^(-1)`
`k=6.9xx10^(-3) s^(-1)`
`k=6.9xx10^(-3) s`
`k=100 s`

ANSWER :B
30398.

The half-life of ._(92)U^(238) " is " 4.5 xx 10^(9) years. After how many years, the amount of ._(92)U^(238) will be reduced to half of its present amount

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`9.0 XX 10^(9)` years
`13.5 xx 10^(9)` years
`.45 xx 10^(9)`years
`4.5 xx 10^(4.5)` years

Solution :Because `t_(1//2) = 4.5 xx 10^(9)` years, so after `4.5xx10^(9)` years the amount of `._(92)U^(238)` will be half decayed
30399.

The half life of ._(92)^(238)U is 4.5 xx 10^(9) years. Uranium emits an alphaparticle to give thorium. Calculate the time required to get the product which contains equal masses of thorium and uranium.

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SOLUTION :`N_(0) = (1)/(238) + (1)/(234)`,`N = (1)/(238)`
Use, `(0.693)/(t_(1//2)) = (2.303)/(t) log_(10) ((N_(0))/(N))`
30400.

The half-life of ._(6)^(14)C is 5730 year. What fraction of its original C^(14) would left after 22920 year of storage?

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0.5
0.25
0.125
0.0625

Answer :D