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1.	The half-life of a radioactive substance is 10 days. This means thatA. The substance completely disintegrates in 20 daysB. The substace completely disintegrates in 40 daysC. `1//8` part of the mass of the substance will be left intact at the end of 40 daysD. `7//8` part of the mass of the substance disintegrates in 30 days
Answer» Correct Answer - D

2.	The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life `30` min decreases to `5 s^(-1)` after `2 h`. The initial count rate wasA. 80 `second^(-1)`B. 625 `second^(-1)`C. 20 `second^(-1)`D. 25 `second^(-1)`
Answer» Correct Answer - A

3.	A nucleus X, initially at rest , undergoes alpha dacay according to the equation , ` _(92)^(A) X rarr _(Z)^(228)Y + alpha ` (a) Find the value of `A` and `Z` in the above process. (b) The alpha particle produced in the above process is found to move in a circular track of radius `0.11 m` in a uniform magnetic field of `3` Tesla find the energy (in MeV) released during the process and the binding energy of the parent nucleus X Given that `: m (Y) = 228.03 u, m(_(0)^(1)n) = 1.0029 u. ` `m (_(2)^(4) He) = 4.003 u , m (_(1)^(1) H) = 1.008 u `
Answer» Correct Answer - [(a) 90, 232; (b) 1823 MeV]

4.	The radioactive nucleus of an element X decays to a stable nucleus of element Y.A graph of the rate of romation of Y against time would look like:A. B. C. D.
Answer» Correct Answer - D

5.	Some amount of a radioactice substance (half-life =10 days ) is spread inside a room and consequently the level of radiation become `50` times the permissible level for normal occupancy of the room. After how many days will the room be safe for occupation?.
Answer» Correct Answer - [169.35 days]

6.	A radioactive nucleus undergoes a series of deacy according to the scheme. `Aoverset(alpha)rarrA_(1)overset(beta^(-))rarrA_(2)overset(alpha)rarrA_(3)overset(gamma)rarrA_(4)` If the mass number and atomic number of `A` are `180` and `172` respectively, what are these numbers for `A_(4)`.
Answer» Correct Answer - [172 and 69]

7.	Suppose a nucleus initally at rest undergoes `alpha` decay according to equation `._(92)^(225)X rarr Y +alpha` At `t=0`, the emitted `alpha`-particles enter a region of space where a uniform magnetic field `vec(B)=B_(0) hat i` and elecrtic field `vec(E)=E_(0) hati` exist. The `alpha`-particles enters in the region with velocity `vec(V)=v_(0)hat j` from `x=0`. At time`t=sqrt3xx10^(6) (m_(0))/(q_(0)E_0)s`, the particle was observed to have speed twice the initial velocity `v_(0)`. Then, find (a) the velocity `v_(0)` of the `alpha`-particles, (b) the initial velocity `v_(0)` of the `alpha`-particle, (c ) the binding energy per nucleon of the `alpha`-particle. `["Given that" m(Y)=221.03 u,m(alpha)=4.003 u,m(n)=1.09u,m(P)=1.008u]`.
Answer» Correct Answer - `[(a) ((q_(alpha)E_(0))/m_(alpha)t)i+v_(0) cos theta hat(j)-v_(0) sin theta hat(k)` where `theta=omegat` and `omega=(q_(alpha)B)/m_(alpha)`, (b) `10^(7) m//s` (c) `8.00 MeV]`

8.	A nuclide `A` undergoes `alpha`-decay and another nuclides `B` undergoes `beta`-decayA. All the `alpha`-particles emitted by A will have almost the same speedB. The `alpha`-particles emitted by A may have widely different speedsC. Al lthe `beta`-particles emitted by B will have almost the same speedD. The `beta`-particles emitted by B will have different speeds
Answer» Correct Answer - A, D

9.	A radioactive nucleus `X `decay to a nucleus `Y` with a decay with a decay Concept `lambda _(x) = 0.1s^(-1) , gamma ` further decay to a stable nucleus Z with a decay constant `lambda_(y) = 1//30 s^(-1)` initialy, there are only X nuclei and their number is `N_(0) = 10^(20)` . Set up the rate equations for the population of `X , Y and Z` The population of `Y` nucleus as a function of time is given by `N_(y) (1) = N_(0) lambda_(x)l(lambda_(x) - lambda_(y))( (exp(- lambda_(y)t))` Find the time at which `N_(y)` is maximum and determine the populations `X and Z` at that instant.
Answer» Correct Answer - [(i) `(dN_(x))/(dt) = - lambda_(x) N_(x) (dN_(y))/(dt) = lambda_(x) N_(x) - lambda_(y) N_(y), (dN_(z))/(dt) = lambda_(y) N_(y)` (ii) 16.48 s, (iii) `N_(x) = 1.92 xx 10^(19), N_(y) = 5.76 xx 10^(19), N_(c) = 2.32 xx 10^(19)`]

10.	A radioactive element `A` with a half-value period of `2` hours decays giving a stable element `Y`. After a time `t` the ratio of `X` and `Y` atoms is `1 : 7` then `t` is :A. 6 hoursB. 8 hoursC. 10 hoursD. 12 hours
Answer» Correct Answer - A

11.	The half-life of a radiactive substance depends upon:A. Its temperatureB. The external pressure on itC. The mass of the substanceD. The strength of the nuclear force between the nucleons of its atom
Answer» Correct Answer - D

12.	The mean lives of a radioactive substance are 1620 years and 405 years for `alpha` emission and `beta` emission respectively. Find out the time during which three fourth of a sample will decay if it is decaying both by `alpha`-emission and `beta`-emission simultaneously. `(log_e4=1.386).`
Answer» Correct Answer - [449 years]

13.	`.^(238)U` decays with a half-life of `4.5 xx10^(9)` years, the decay series eventaully ending at `.^(206)Pb`, which is stable. `A` rock sample analysis shows that the ratio of the number of atoms of `.^(206)Pb` to `.^(238)U` is 0.0058. Assuming that all the `.^(206)Pb` is prodduced by the decay of `.^(238)U` and that all other half-lives on the chain are negligilbe, the age of the rock sample is `(1n 1.0058 =5.78 xx10^(-3))`.
Answer» Correct Answer - `[38 xx 10^(6) yrs]`

14.	A nucleus undergoes a series of decay according to the scheme `A overset(alpha)(rarr) B overset(beta)(rarr)C overset(alpha)(rarr)D overset(gamma)(rarr) E` Atomic number and mass number of E are 69 and 172A. Atomic number of A is 72B. Mass number of B is 176C. Atomic number of D is 69D. Atomic number of C is 69
Answer» Correct Answer - B, C

15.	In a reactor, an element X decays to a radioactive element Y, at a constant rate r atoms per second. Each decay reaction releases energy `E_(1)`. Half life of element Y is equal to T and decays to a stable element. During each decay of Y, energy `E_(2)` is released. If at `t=0`, there was no atom of element Y and all the energy released is used in the reactor for generation of electrical power with efficiency `eta`, calculate electrical power generation in the reactor (i) at time `t` and (ii) in steady state.
Answer» Correct Answer - `[(i)" "eta r[E_(1)+E_(2)(1-e^((t log 2)/T))], (ii)" "eta r(E_(1)+E_(2))]`

16.	An element` X` decays , first by positron emission and then two `alpha`-particles are emitted in successive radiactive decay. If the product nucleus has a mass number `229` and atomic number `89`, the mass number and atomic number of element ` X` are.A. 237,93B. 237,94C. 221,84D. 237,92
Answer» Correct Answer - B

17.	A radio nuclide consists of two isotopes. One of the isotopes decays by `alpha`-emission and other by `beta`-emission with half-lives `T_1=405s` and `T_2=1620s`, respectively. At `t=0`, probabilities of getting `alpha` and `beta`-particles from the radio nuclide are equal . Calculate their respective probabilities at `t=1620s`. If at `t=0`, total number of nuclei in the radio nuclide are `N_0`. Calculate the time t when total number of nuclei remained undecayed becomes equal to `N_0//2`. `log_(10)2=0.3010`, `log_(10)5.94=0.7742` and `x^4+4x-2.5=0`, `x=0.594`
Answer» Correct Answer - `[1/9, 8/9, 1215 s]`

18.	Carbon (Z=6) with mass number 11 decays to boron (Z=5).(a) Is it a `beta^+` -decay? (b) the half-life of the decay scheme is 20.3 minutes .How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11(by the number pf atoms )converts itself into a mixture of 10% carbon-11 and 90% boron -11?
Answer» Correct Answer - `[beta^(+), 64 min]`