Some of the important questions are prepared from this Atoms and Nuclei. In this question paper, questions are prepared from the book back and previous year questions.

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Questions:

Generic 3

4 x 3 = 12

The nuclear radius of \(_{ 8 }{ { O }^{ 16 } }\) is \(3\times { 10 }^{ -15 }m\) . What is its nuclear mass density?

Find the effective mass of a photon if the frequency of the radiation is \(6\times { 10 }^{ 14 }Hz\) .

What is Bohr's frequency condition?

'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.

Multiple Choice Question

9 x 1 = 9

A sample of a radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is

(a)

1.35 g

(b)

2.50 g

(c)

3.70 g

(d)

6.30 g

In the Bohr model of the hydrogen atom, let R, V and E represent the radius of the orbit, speed of the \({ e }^{ - }\) and total energy of the \({ e }^{ - }\) respectively. Which of the following quantities are proportional to the quantum number n?

(a)

(b)

(c)

\(\frac { V }{ E } \)

(d)

\(\frac { R }{ E } \)

A deutron is bombarded on \(_{ 8 }{ { O }^{ 16 } }\) nucleus and an \(\alpha \) particle is emitted. The product nucleus is

(a)

\(_{ 7 }{ { N }^{ 14 } }\)

(b)

\(_{ 7 }{ { N }^{ 13 } }\)

(c)

\(_{ 4 }{ { Be }^{ 9 } }\)

(d)

\(_{ 5 }{ { B }^{ 10 } }\)

The mass number of a nucleus is :

(a)

always less than its atomic number

(b)

always more than its atomic number

(c)

sometimes equal to its atomic number

(d)

sometimes more than and sometimes equal to its atomic number

The activity of a freshly prepared radioactive sample is \({ 10 }^{ 10 }\) disintegrations per second, whose mean life is \({ 10 }^{ 9 }s.\) The mass of an atom of this radioisotope is \({ 10 }^{ -25 }kg.\) The mass (in mg) of the radioactive sample is :

(a)

(b)

(c)

(d)

10.

The Balmer series for the H-atom can be observed

(a)

if we measure the frequencies of light emitted when an excited atom falls to the ground state

(b)

if we measure the frequencies of light emitted due to transitions between excited states and the first excited state

(c)

in any transition in a H-atom

(d)

as a sequence of frequencies with the higher frequencies getting closely packed.

11.

The Bohr model for the spectre of a H-atom

(a)

will not be applicable to hydrogen in the molecular form

(b)

will not be applicable as it is for a He-atom

(c)

is valid only at room temperature

(d)

predicts continuous as well as discrete spectral lines

12.

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.

13.

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

Generic 2

4 x 2 = 8

14.

Using Rutherford's model of the atom, derive the expression for the total energy of the electron in H-atom. What is the significance of total negative energy possessed by the electron?

15.

Draw a plot of BE/A versus mass number A for Use this graph to explain the release of enegry in the process of nuclear fusion of two light nuclei.

16.

Show that the decay rate R of a sample of radionuclide is related to the number of radioactive nuclei N at the same instant by the expression \(R=\lambda N\).

17.

For a given impact parameter b, does the angle of deflection increase or decrease with increase in energy?

Fill up / 1 Marks

5 x 1 = 5

18.

Radioactivity is the property by virtue of which ___________ without being forced by ___________.

19.

Isotopes of an element are the atoms ___________ which have __________ but ___________.

20.

Orbital velocity of electron in outer orbit is ____________ as compared to its value in____________.

21.

Lyman series lies in __________ region and Balmer series lies in ________ region of hydrogen spectrum.

22.

According to Thomson model, the entire mass and positive charge of an atom are distributed ____________ in a ___________ of radius ___________.

Generic 5

2 x 5 = 10

23.

Poonam's mother is diagnosed cancer. The attending physician told her that she has to undergo radiotherapy. While telling her the side effects of the treatment, the doctor told that her beautiful hair may fall and she may become bald. Poonam's mother refuses to get the treatment.
Read the above passage and answer the following questions:
(i) What would you do if you were in Poonam's place?
(ii) What values are associated with your attitude?

24.

A nuclear reactor is a powerful device, wherein nuclear energy is utilised for peaceful purposes. It is based upon controlled nuclear chain reaction. The nuclear chain reaction is controlled by the use of control rods (of boron or cadmium) and moderators like heavy water, graphite, etc. The whole reactor is protected with concrete walls 2 to 2.5 metre thick, so that radiations emitted during nuclear reactions may not produce harmful effects.
Read the above passage and answer the following questions:
(i) Give any two merits of nuclear reactors.
(ii) What is radiactive waste?
(iii) Why do people often oppose the location site of a nuclear reactor? What do you suggest?

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Answers Key:

Generic 3

4 x 3 = 12

\(2.359\times { 10 }^{ 17 }\quad kg/{ m }^{ 3 }\)
Here,\(R=3\times { 10 }^{ -15 }m,\quad \rho =?\)
Mass, \(m=16 \ amu \ =\ 16\times 1.66\times { 10 }^{ -27 }\ kg\)
\(\rho =\frac { m }{ V } =\frac { m }{ \frac { 4 }{ 3 } \pi { R }^{ 3 } }\)
\( =\frac { 3\times 16\times 1.66\times { 10 }^{ -27 } }{ 4\times 3.14{ \left( 3\times { 10 }^{ -15 } \right) }^{ 3 } } =2.359\times { 10 }^{ 17 }\ kg/{ m }^{ 3 }\)

\(4.4\times { 10 }^{ -36 }\ kg\)
\(E=hv=m{ c }^{ 2 }\)
\(\therefore \ m=\frac { hv }{ { c }^{ 2 } } =\frac { 6.6\times { 10 }^{ -34 }\times 6\times { 10 }^{ 14 } }{ { \left( 3\times { 10 }^{ 8 } \right) }^{ 2 } } \)
\(=4.4\times { 10 }^{ -36 } \ kg\)

Whenever an electron jumps from higher energy orbit En₂ to lower energy orbit En_1,the frequency of the radiation emitted is given by hv = En₂ - En₂. It is called Bohr's frequency condition.

1 : 1

Multiple Choice Question

9 x 1 = 9

(a)
1.35 g

(a)
VR

(a)
\(_{ 7 }{ { N }^{ 14 } }\)

(a)
1

10.

(b)
if we measure the frequencies of light emitted due to transitions between excited states and the first excited state

11.

(b)
will not be applicable as it is for a He-atom

12.

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

13.

Generic 2

4 x 2 = 8

14.

Total energy = P.E. + K.E.
\(=-\frac { 1 }{ { 4\pi \epsilon }_{ 0 } } \frac { { Ze }^{ 2 } }{ r } +\frac { 1 }{ 2 } { m }v^{ 2 }=\frac { -1 }{ { 4\pi \epsilon }_{ 0 } } \frac { { Ze }^{ 2 } }{ r } +\frac { 1 }{ { 8\pi \epsilon }_{ 0 } } \frac { { Ze }^{ 2 } }{ r } \)
\(=-\frac { 1 }{ 2 } .\frac { 1 }{ { 4\pi \epsilon }_{ 0 } } \frac { { Ze }^{ 2 } }{ r } =-\frac { 1 }{ { 8\pi \epsilon }_{ 0 } } \frac { { Ze }^{ 2 } }{ r } \)
Negative sign implies that electron - nucleus form a bound system.

15.

The above curve shows that
(i) when a heavy nucleus breaks into two medium sized nuclei(in nuclear fission)the BE/nucleon increases resulting in the release of energy
(ii) When two small nuclei combine to form relatively bigger nuclear fusion BE/nucleon increases ,resulting in the release of energy.

16.

According to radioactive decay law.
\(R=-\frac { dN }{ dt } =\frac { -d }{ dt } ({ N }_{ 0 }{ e }^{ -\lambda t })=\lambda { N }_{ 0 }{ e }^{ -\lambda t }\ =\lambda N\).
Rate of decay,
\(R=-\frac { dN }{ dt } =\frac { -d }{ dt } ({ N }_{ 0 }{ e }^{ -\lambda t })=\lambda { N }_{ 0 }{ e }^{ -\lambda t }\ =\lambda N\)

17.

From \(b=\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } \frac { Z{ e }^{ 2 }cot \ { \theta }/{ 2 } }{ E } \)
For given value of b, when E is increased, \(cot\frac { \theta }{ 2 } \)increases; \(tan\frac { \theta }{ 2 } \) decreases; \(\theta \) decreases.

Fill up / 1 Marks

5 x 1 = 5

18.

()
a heavy element decays; any external agent to do so.

19.

()
of an element; same atomic number; different atomic weights

20.

()
less; inner orbits,

21.

()
ultra-violet; visible

22.

()
uniformly; sphere; of the order of \({ 10 }^{ -10 }m\)

Generic 5

2 x 5 = 10

23.

(i) If I were in Poonam's place, I would tell my mother that treatment of cancer is a must. Hair fall is a temporary effect and the hair would grow slowly after the therapy. Convincing my mother to get the treatment, using all sorts of reasoning will be my top priority.
(ii) Concern for my mother's health is of utmost importance. I will not mind taking help from specialists to convince my mother for getting the treatment.

24.

(i) Nuclear reactors are used in electric power generation. They are also used to produce radioactive isotopes which have applications in medicine, industry and agriculture.
(ii) Radioactive waste consists of fission products and transuranic elements such as plutonium and americium. This waste is extremely hazardous to all forms of life on earth.
(iii) People often oppose the location site of a nuclear reactor because any leakage of nuclear radiations can affect adversely miles of area surrounding it. Elaborate safety measures are needed not only for reactor operations, but also for handling and disposal of radioactive waste.
I would suggest that Government must take stringent safety measures and assure people of safeguards in the event of nuclear accidents. At the same time, people must also be educated accordingly.