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201.

In a sample of hydrogen atoms, all the atoms exist in two energy levels A and B. A is the ground level and B is some higher energy level. These atoms absorb photons of energy 2.7 eV and attain a higher energy level C.After this, these atoms emit photons of six different energies. Some of these photon energies are higher than 2.7 eV, some equal to 2.7 eV and some are loss than 2.7 eV. The principal quantum number corresponding to energy level B isA. 1B. 2C. 3D. 4

Answer» Correct Answer - B
202.

In a sample of hydrogen atoms, all the atoms exist in two energy levels A and B. A is the ground level and B is some higher energy level. These atoms absorb photons of energy 2.7 eV and attain a higher energy level C.After this, these atoms emit photons of six different energies. Some of these photon energies are higher than 2.7 eV, some equal to 2.7 eV and some are loss than 2.7 eV. The principal quantum number corresponding to energy level C isA. 1B. 2C. 3D. 4

Answer» Correct Answer - D
203.

In a sample of hydrogen atoms, all the atoms exist in two energy levels A and B. A is the ground level and B is some higher energy level. These atoms absorb photons of energy 2.7 eV and attain a higher energy level C.After this, these atoms emit photons of six different energies. Some of these photon energies are higher than 2.7 eV, some equal to 2.7 eV and some are loss than 2.7 eV. The atomic number of these atoms isA. 1B. 2C. 3D. 4

Answer» Correct Answer - A
204.

In a sample of hydrogen atoms, all the atoms exist in two energy levels A and B. A is the ground level and B is some higher energy level. These atoms absorb photons of energy 2.7 eV and attain a higher energy level C.After this, these atoms emit photons of six different energies. Some of these photon energies are higher than 2.7 eV, some equal to 2.7 eV and some are loss than 2.7 eV. The longest wavelength emitted in the radiation spectrum observed isA. 18761 ÅB. 1216 ÅC. 6500 ÅD. 5752 Å

Answer» Correct Answer - A
205.

What is the value of Rydberg’s constant? 

Answer»

The value of Rydberg’s constant :

R = 1.097 x 107 m-1

206.

The total energy of an electron in the first excited state of the hydrogen atom is -3.4eV. What is the potential energy of the electron in this state ?

Answer» In `1^(st)` orbit, E=-3.4 eV
Total energy `E=(KZe^(2))/(2r)-(KZe^(2))/(r )`
`(KZ e^(2))/(r )=U` (say)
`E=(u)/(2)-u=(-u)/(2)`
`U=-2E`
`therefore U=-2xx-3.4=6.8 eV`.
207.

What is wave number of spectral line? 

Answer»

Wave number represents number of waves present in one metre length of the medium. 

208.

What would be the charge in radius of `n^"th"` orbit, if the mass of electron reduces to half of its original value ?

Answer» As `r prop 1/m` , therefore radius would be doubled.
209.

Total energy of an electron in an atom is negative . What does it signify ?

Answer» Negative energy signifies that force between electron and nucleus is attractive. Electron is bound to the nucleus .
210.

What would be the ratio of product of velocity and time period of electron orbiting in `2^"nd"` and `3^"rd"` stable orbits ?

Answer» Time period x Velocity `prop n^2`
`therefore (T_2V_2)/(T_3V_3)=2^2/3^2=4/9`
211.

with the help of Rydberg formula find the wavelength of first line of Pfund series .

Answer» `1/lambda=R(1/n_f^2- 1/n_i^2)`
For first line of Pfund series, `n_i`=6 and `n_f`=5
`therefore 1/lambda=R(1/5^2-1/6^2)`
`rArr lambda=900/"11R"`
212.

The shortest wavelength which can be obtained in hydrogen spectrum `(R=10 ^(7) m^(-1))`A. 1000 ÅB. 8000 ÅC. 1300 ÅD. 2100 Å

Answer» Correct Answer - A
The wavelemgth can be given as
`" "(1)/(lambda)=Z^(2)R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
For `lambda` to the shortest `((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))` should be maximum
So, `" " n_(2)=oo and n_(1)=1`
Now, from Eq. (i) we get
`(1)/(lambda)=R((1)/(1))rArrlambda=(1)/(R)=(1)/(10^(7))m~~ 1000Å`
213.

Assertion Angular momentum of single electron in any orbit or hydrogen type atom is independent of the atomic number of the element. Reason In ground state angular momentum is minimumA. If both Assertion and Reason ar true and Reason is the correct explanation of Assertion.B. If both Assertion and Reason are true but Reason is not correct explanation of AssertionC. If Assertion is true by Reason is false.D. If Assertion is false but Reason is true.

Answer» Correct Answer - B
`L=n((h)/(2pi))i.e.,Lpropn.` In ground state n=1
so L= minimum.
214.

If scattering particles are `56` for `90^(@)` angle than this will be at `60^(@)` angleA. 224B. 256C. 98D. 108

Answer» Correct Answer - A
Accroding to scattering formula
`" " Nprop(1)/(sin^(4)(theta//2))rArr(N_(2))/(N_(1))=[(sin(theta_(1)//2))/(sin(theta_(2)//2))]^(4)`
`rArr" " (N_(2))/(N_(1))=[(sin.(90^(@))/(2))/(sin.(60^(@))/(2))]^(4)=[(sin 45^(@))/(sin30^(@))]^(4)`
`rArr " " N_(2)=(sqrt(2))^(4)xxN_(1)=4xx56=224`
215.

A radioactive sample consist of two distinct spices having equal number of atoms initially. The mean life one spices is τ and that of other 5τ. The decay products in both cases are stable. The following figure shows graphs P, Q, R, S the plot of the total number of radioactive nuclei as a function of time. Which of the graphs P, Q, R and S represent the best form of the plot?(1) P (2) Q (3) R (4) S

Answer»

Correct option : (4) S

Explanation:

Since it is the process of radioactivity decay the total number of atoms cannot remains constant (as in option 1). Also the total number of atoms cannot ever increase (as in option 2 and 3). The total number of atoms can only decrease with time. Hence option (4) is the best plot.

216.

Which of the following cannot be the value of ionisation energy for a hydrogen atom ?A. 0.85 eVB. 3.4 eVC. 1.51 eVD. 0.27 eV

Answer» Correct Answer - D
217.

Define ionisation energy. What is the value for a hydrogen atom?A. `3.4 Ev`B. `10.4 Ev`C. `12.09 Ev`D. `13.6 Ev`

Answer» Correct Answer - D
The minimum energy required to free the electron from the ground state of the hydrogen atom is called the ionisation energy of hydrogen atom, its value is `13.6eV`.
218.

The second member of Lyman series in hydrogen spectrum has wavelength `5400 Å`. Find the wavelength of first member.

Answer» `(1)/(lamda)=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
For second member of Lyman series,
`(1)/(5400)=R((1)/(1^(2))-(1)/(3^(2)))rArr(1)/(5400)=(8R)/(9)rarr(1)`
For first member of Lyman series,
`(1)/(lamda^(1))=R((1)/(1^(2))-(1)/(2^(2)))`
`(1)/(lamda^(1))=(3R)/(4)" "rarr(2)`
`((1))/((2))rArr(lamda^(1))/(5400)=(8R)/(9)xx(4)/(3R)`
`therefore lamda^(1)=(32)/(27)xx5400=6400 Å`.
219.

Calculate the shortest wavelength of Balmer series. Or Calculate the wavelength of the Balmer series limit. Given : `R = 10970000 m^(-1)`.

Answer» `(1)/(lamda)=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`R=10970000=1.097xx10^(7) ms^(-1)`
For Balmer series limit `n_(1)=2 and n_(2)=prop`
`(1)/(lamda)=R((1)/(2^(2))-(1)/(prop))rArr(1)/(lamda)=(R )/(4)`
`lamda=(4)/(R )=(4)/(1.097xx10^(7))=3646.3 Å`.
220.

Wavelength corresponding to series limit isA. `(1)/(lambda)=(2R)/(n)`B. `(1)/(lambda)=(R^(2))/(n^(2))`C. `(1)/(lambda)=(R^(2))/(n^(2))`D. `(1)/(lambda)=(R)/(n)`

Answer» Correct Answer - C
221.

In which of the following transition will the wavelength be minimum ?A. n=5 to n=4B. n=4 to n=3C. n=3 to n=2D. n=2 to n=1

Answer» Correct Answer - D
The wavelength will be minimum ffor which `((1)/(n_f^(2))-(1)/(ni^(2)))` is maximum.
222.

Find the minimum wavelength emitted by a hydrogen atom due to electronic transition.

Answer» Solve , `1/lambda=R(1-1/oo)`
`R to ` Rydberg constant
223.

A sample of a radioactive substance has `10^(6)` radioactive nuclei. Its half life time is 20 s How many nuclei will remain after 10 s ?

Answer» Correct Answer - `7xx 10^(5)` (approx)
224.

4g of a radioactive material of half life 10 years is kept in a store for 15 years. How much material is disntegrated ?

Answer» Correct Answer - 2.5855 g
225.

Obtain approximately the ratio of the radii of iron `._(26)Fe^(56)` and calcium `._(20)Ca^(40)`. What is the approximate ratio of their nuclear mass densities?

Answer» Correct Answer - 1.12, 1
226.

Define mass defect and state an expression for it.

Answer»

The difference between the sum of the masses of all the individual nucleons in a nucleus and the mass of the nucleus is known as the mass defect.

Mass defect, ∆m = (Zmp+ Nmn) – M where mp is the proton mass, mn is the neutron mass, M is the mass of the nucleus, Z is the atomic number and N = A – Z is the neutron number.

227.

Calculate the mass defect and binding energy of \(^{59}_{27}Co\) which has a nucleus of mass 58.933 u. [Take mp = 1.0078 u, mn = 1.0087 u]

Answer»

Data: mp = 1.0078 u, mn = 1.0087 u, 

mCo = 58.933 u,

1 u = 931.5 MeV/c2

For \(^{59}_{27}Co\), A = 59, Z = 27

∴ N = A – Z = 59 – 27 = 32

The mass defect,

∆m=(Zmp + Nn) – mCo

= (27 × 1.0078 + 32 × 1.0087) – 58.933 

= (27.2106 + 32.2784) – 58.933 

= 59.4890 – 58.933 = 0.556 u 

∴ The binding energy

= ∆mc2

= 0.556 uc2 × 931.5 MeV/uc2

= 517.8 MeV

228.

A nucleus of `Ux_(1)` has a life of 24.1 days. How long a sample of `Ux_(2)` will take to change to 90 % of it to `Ux_(2)` ?

Answer» Correct Answer - 80 days
229.

What is nuclear energy?

Answer»

Energy released in a nuclear reaction such as a spontaneous or induced nuclear fission, or nuclear fusion, or in interaction of two nuclei, is called nuclear energy.

[Note : It is far greater from that released in a chemical reaction.]

230.

If the number of nuclei of a radioactive substance becomes 1/e times the initial number in 10 days, what is the decay constant of the substance ?

Answer»

N(t) = N0e-λt

∴ In this case,

\(\cfrac{N(t)}{N_0}\) = \(\cfrac1e\) = e-λt \(\cfrac1{e^{λt}}\)

∴ λt  = 1

∴ The decay constant,

λ = \(\cfrac1t\) = \(\cfrac1{10}\) day-1

= 0.1 day-1

231.

The binding energy of a H-atom considering an electron moving around a fixed nuclei (proton), is `B = - (me^(4))/(8n^(2)epsi_(0)^(2)h^(2))` (m= electron mass) If one decides to work in a frame of refrence where the electron is at rest, the proton would be movig around it. By similar arguments, the binding energy would be : `B = - (me^(4))/(8n^(2)epsi_(0)^(2)h^(2))` (M = proton mass) This last expression is not correct, becauseA. n would not be integralB. bohr- quantisation applies only to electronC. the frame in which the electron is at rest is not inertialD. the motion of the proton would not be in circular orbits, even approximately

Answer» Correct Answer - C
In the frame of reference, where electron is at rest the given expression cannot be true for binding energy as the frame in which electron is at rest would not be inertial. In hydrogen atom, electron revolving around a fixed proton nucleus has some centripetal acceleration.
232.

In which model atoms become unstable? 

Answer»

In Rutherford atom model. (An accelerating electron radiates energy and spiral around the nucleus. Ultimately electrons should fall inside the nucleus.) 

233.

What is meant by a stationary orbit?

Answer»

n the Bohr model of the hydrogen atom, a stationary orbit refers to any of the discrete allowed orbits such that the electron does not radiate energy while it is in such orbits.

234.

What is a stationary orbit? 

Answer»

A stationary orbit is one in which the revolving electron does not radiate energy. 

235.

Are the electron orbits equally spaced? 

Answer»

No. Electron orbits are unequally spaced.

236.

Give the relation between radius and principle Quantum number of an atom. 

Answer»

Relation between radius and principle Quantum number of an atom. 

rn ∝ n2

237.

What is the relation between the energy of an electron and the principle Quantum number? 

Answer»

Relation between the energy of an electron and the principle Quantum number

En ∝ 1/n2  

238.

What is excited state of an atom?

Answer»

When atom is given sufficient energy, the transition takes place to an orbit of higher energy. The atom is then said to be in an excited state. 

239.

Hydrogen atom is exited from ground state to another state with principal quantum number equal to `4` Then the number of spectral line in the emission spectra will beA. 2B. 3C. 5D. 6

Answer» Correct Answer - D
If n-4, then
lines `=(n(n-1))/(2)=6`
240.

In column-I name of the spectral series are given and column-II gives wavelength formula corresponding to series and region of series.

Answer» Correct Answer - A::B::C::D
241.

The orbital frequency of an electron in the hydrogen atom is proportional toA. `n^(3)`B. `n^(-3)`C. nD. `n^(0)`

Answer» Correct Answer - D
Time period of orbital motion electorn `T=(4epsi_(0)^(2)n^(3)h^(3))/(mZ^(2)e^(4))`
`rArrTpropn^(3)rArr(1)/("Frequency(f)")propn^(3)`
`rArrfpropn^(-3)`
242.

Column-II give some quantities associated with electron of hydrogen like atom. The quantities are proportional to entries given in column-I . Match the column appropriately

Answer» Correct Answer - A::B::C::D
243.

Regarding the spectrum of hydrogen, match the entries in column-I with all the entries in column-II. Match the following :

Answer» Correct Answer - A::B::C::D
244.

In the Bohr model of the hydrogen atgomA. The radius of nth orbit is proportional to `n^(2)`B. The total energy of electron in nth orbit is proportional to nC. The angular momentum of an electron in an orbit is an intergal multiple of `h//2pi`D. The magnitude of the potential energy of an electron in any orbit is greater than its kinetic energy

Answer» Correct Answer - B
245.

A gas of hydrogen - like ion is perpendicular in such a way that ions are only in the ground state and the first excite state. A monochromatic light of wavelength `1216 Å` is absorved by the ions. The ions are lifted to higher excited state and emit emit radiation of six wavelength , some higher and some lower than the incident wavelength. Find the principal quantum number of the excited state identify the nuclear charge on the ions . Calculate the values of the maximum and minimum wavelengths.

Answer» Correct Answer - D
246.

Which of the following parameters are the same for all hydrogen like atoms and ions in their ground state?A. Radius of the orbitB. speed of the electronsC. Energy of the atomD. Orbital angular momentum of the electron

Answer» Correct Answer - D
247.

Assertion A beam of charged particles is employed in the treatment of cancer. Reason Charged particles on passing through a material medium loss their energy by causing ionisation of the atoms along their path.A. If both Assertion and Reason are true and Reason is the correct explanation of Assetion.B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.C. If Assetion is true but Reason is false.D. If both Assertion and Reason are false.

Answer» Correct Answer - B
A raditation consists of a beam of a charged particles. When radiation is used for cancer treatement , them on falling upon the concerous , it destryos, cancer cells.
248.

In Bohr model of hydrogen atom, the force on the electron depends on the principal quantum number (n) asA. independent of nB. `Fprop(1)/(n^(5))`C. `Fprop(1)/(n^(4))`D. `Fprop(1)/(n^(3))`

Answer» Correct Answer - C
We have, `Fprop(v^(2))/(r)`
Also, `vprop(1)/(n)an dr propn^(2)rArrFprop(1)/(n^(4))`
249.

The wavelength of `K_(alpha)` X-ray for an element is 21.3 pm. It takes 12.5 ke V to knock out an electron out an electron from the L-shell of the atom of the element. What should be the minimum accelerating voltage across on X-ray tube having the element as target which allows production of `K_(alpha)` X-ray?

Answer» Since `E_(K)-E_(L)=(hc)/(lambda_(K_(alpha)))`
It is given that `lambda_(K_(alpha))=21.3"pm" =0.0213 "nm"`
Also, `" " E(eV) =(1242)/(lambda(nm))=(1242)/(0.0213)=58.3 eV`
`rArr" " E_(K)-E_(L)=E`
`rArr" " E_(K)-12.5=58.3`
`rArr" "E_(K)=70.8 keV`
`:.` Acceleration potential =70.8 keV
250.

Find the absolute mass of oxygen.

Answer»

The atomic mass of oxygen is 16u

We know 1u = 1.6605 x 10–24 g

Therefore, Absolute mass of oxygen = 1.6605 x 10–24 x 16 g

= 26.568 x 10–24 = 2.6568 x 10–25 g