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Published on: 02/11/2025

Question Set C

CBSE 12th Standard Physics Atoms HOT Questions Study Material - QB365

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Std: 12th Standard CBSE - Physics

chapter: Atoms - HOT Questions

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Questions:

'The half life \(_{ 6 }^{ 14 }{ C }\) is 5700 years.' What does it mean ?
Two radioactive nuclei X and Y initially contain an equal number of atoms. Their half life is 1 hour and 2 hours respectively. Calculate the ratio of their rates of disintegration after two hours.

An \(\alpha \)- particle of K.E.\({ 10 }^{ -12 }\)J exhibits backscattering from a gold nucleus Z = 79. What can be the maximum possible radius of the gold nucleus?

Calculate shortest wavelength of Balmer series. Given \(R=1.097\times { 10 }^{ 7 }{ m }^{ -1 }\).

A radioactive material is reduced to of\(\frac { 1 }{ 16 } \) its original amount in 4 days. How much material should one begin with so that of \(4\times { 10 }^{ -3 }kg\) the material is left after 6 days?

Taking the Bohr radius as a₀ = 53pm, the radius of Li⁺⁺ ion its ground state, on the basis of Bohr's model, will be about

(a)

53pm

(b)

27pm

(c)

18pm

(d)

13pm

O₂ molecule consists of two oxygen atoms.In the molecule, nuclear force between the nuclei of the two atoms

(a)

is not important because nuclear forces are short-ranged

(b)

is as important as electrostatic force for binding the two atoms

(c)

cancels the repulsive electrostatic force between the nuclei

(d)

is not important because oxygen nucleus have equal number of neutrons and protons.

Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom,

(a)

because of energy conservation

(b)

without simultaneously releasing energy in the form of radiation

(c)

because of momentum conservation

(d)

because of angular momentum conservation.

Name the spectral series of hydrogen atom, which is in infrared region.

What is the impact parameter for scattering of \(\alpha \)- particle by \(180°\)?

10.

The electron, in a hydrogen atom, is in its second excited state. Calculated the wavelength of the lines in the Lyman series, that can be emitted through the permissible transitions of this electron. (Given the value of Rydberg constant, R = 1.1 x 10⁷ m^-1)

11.

Does the ratio of neutrons and protons in the nucleus increase, decreases or remain the same after the emission of \(\alpha\) – particles?

12.

A radio isotope of silver has a half life of 20 minutes. What fraction of the original mass would remain after one hour?

13.

Can a single nucleus emit \(\alpha\) – particle, \(\beta\) – particle and a γ – rays together?

14.

Write nuclear equations for
a) The \(\alpha\)-decay of ²²⁶Ra₈₈
b) The \(\beta\)^- -decay of ³²P₁₅
c) The \(\beta\)⁺ decay of ³²P₁₅

15.

A neutron is absorbed by a ⁶Li3 nucleus with the subsequent emission of an alpha particle.
i) Write the corresponding nuclear reactions.
ii) Calculate the energy released in MeV, in this reaction.
Given mass ⁶Li3 = 6.0151264; mass (neutron) = 1.00966544
Mass (alpha particle) = 4.00260444 and mass(triton) = 3.01000004

16.

Nuclear fission is the phenomenon of splitting of a heavy nucleus into two or more lighter nuclei. Nuclear fussion is the phenomenon of fusing two or more lighter nuclei to form a single heavy nucleus. In both these processes, a certain mass \(\left( \Delta m \right) \) disappears, which appears in the form of nuclear energy, \(E=\left( \Delta m \right) { c }^{ 2 }.\) The release of energy is so sudden that it cannot be controlled. This causes havoc. Nuclear fission is the basis of an atom bomb and nuclear fusion is the basis of a nydrogen bomb. A powerful device, called Nuclear Reactor has been developed, where in nuclear energy produced is utilised for constructive purposes.
Read the above passage and answer the following questions:
(i) How much energy is released in the fission of one nucleus of \({ U }^{ 235 }\) and in how much time?
(ii) Give an estimate of devastation potential of an atomic explosion.
(iii) Should we ban nuclear research in this field? Give your views briefly.

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Answers Key:

1 : 1

\(3.64\times { 10 }^{ -14 }m\)
Here, K.E \(=\frac { 1 }{ 2 } m{ v }^{ 2 }={ 10 }^{ -12 }J,\ Z=79\)
Maximum possible radius=distance of closest approach
\({ r }_{ 0 }=\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } \frac { (Ze)(2e) }{ \left( \frac { 1 }{ 2 } m{ v }^{ 2 } \right) }\)
\( \\ =\frac { 9\times { 10 }^{ 9 }\times 2\times 79{ (1.6\times { 10 }^{ -19 }) }^{ 2 } }{ { 10 }^{ -12 } }\)
\(=3.64\times { 10 }^{ -14 }m\)

\(3646.8\mathring { A } \)
\(Take \ { n }_{ 1 }=2 \ and \ { n }_{ 2 }=\infty \)

\(\frac { N }{ { N }_{ 0 } } =\frac { 1 }{ 16 } ,\ t=4\quad days,{ N }_{ 0 }=?N=4\times { 10 }^{ -3 }kg.\)
\(As \ \frac { N }{ { N }_{ 0 } } ={ \left( \frac { 1 }{ 2 } \right) }^{ n }=\frac { 1 }{ 16 } ={ \left( \frac { 1 }{ 2 } \right) }^{ 4 },n=4or\frac { t }{ T } =4,\)
\(T=\frac { t }{ 4 } =\frac { 4 }{ 4 } =1 \ day\)
\(Again, \ \frac { N }{ { N }_{ 0 } } ={ \left( \frac { 1 }{ 2 } \right) }^{ n }={ \left( \frac { 1 }{ 2 } \right) }^{ 1/T }={ \left( \frac { 1 }{ 2 } \right) }^{ 6/1 }=\frac { 1 }{ 64 }\)
\({ N }_{ 0 }=64N=64\times 4\times { 10 }^{ -3 }kg=0.256kg\)

(a)
is not important because nuclear forces are short-ranged

(b)
without simultaneously releasing energy in the form of radiation

Paschen Series, Brackett Series, and Pfund Series lie in infrared region.

Zero. This follows from the relation \(b=\frac { Z{ e }^{ 2 }cot\quad { \theta }/{ 2 } }{ 4\pi { \epsilon }_{ 0 }\left( \frac { 1 }{ 2 } m{ v }^{ 2 } \right) } \)

10.

For second excited state, n = 3
Hence two possible transition of the Lyman series: 3→1 and 2→1
Wavelength for transition 3→1, n_f = 1, n_i = 3
\(\frac { 1 }{ \lambda } =R\left( \frac { 1 }{ { n }_{ f }^{ 2 } } -\frac { 1 }{ { n }_{ i }^{ 2 } } \right) \)
\(\frac { 1 }{ \lambda } =1.1\times { 10 }^{ 7 }\left( \frac { 1 }{ 1 } -\frac { 1 }{ 9 } \right) \)
\(=1.1\times { 10 }^{ 7 }\left( \frac { 8 }{ 9 } \right) \)
⇒ λ = \(\frac { 9 }{ 8\times 1.1\times { 10 }^{ -7 } } \)
= 1.023 x 10^-7
= 102. 3nm
For transition 2→1, n_f =1, n_i=2
\(\frac { 1 }{ \lambda } =1.1\times { 10 }^{ 7 }\left( 1-\frac { 1 }{ 4 } \right) \)
⇒ λ = 212 nm

11.

The ratio of neutrons to proton ratio increases, after the emission of a α - Particle

12.

T = 20 minutes t = 60 minutes
N/No = (1/2)ⁿ = (1/2)60/20 = (1/2)³ =1/8
After one hour, 1/8th of the original mass would remain

13.

No a nucleus either emits a α – particle or a β – particle and if left in the exited state, it may emit γ – ray also.

14.

a) ²²⁶Ra₈₈-----------------\(\rightarrow\)-²²²Rn₈₆ + ⁴He₂
b) ³²P₁₅------------------ \(\rightarrow\)³²S₁₆ + ⁰e_-1 + \(\gamma \)
c) ³²p¹⁵------------------- \(\rightarrow\)¹¹B₅+⁰e₊₁+ \(\gamma \)

15.

(i) 6Li3 + 1no \(\rightarrow\)3H1 + 4He2 +Q (energy)
(ii) Q = \(\triangle\)mx931 MeV
Where \(\triangle\)m = 6.01512+1.0086654-4.0026044-3.0100000

16.

(i) From the fission of a single nucleus of \(_{ 92 }{ { { U }^{ 235 } } }\); 200 MeV energy is released in \({ 10 }^{ -9 }\) second, i.e., almost instantly.
(ii) First atomic explosion occurred in 1945 when an atom bomb was dropped on the city of Hiroshima, Japan. This resulted in the killing of about 66000 people and grievous injury to an equal number. 2/3rd of city structures were smashed and so on.
(iii) No, the research must go on. But we must investigate ways and means for harnessing the enormous amount of nuclear energy for peaceful purposes. Nuclear reactor is an outcome of that research.