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Nuclei

Multiple Choice Questions

1.

A radioactive substance decays to 1/16th of its initial activity in 40 days. The half-life of the radioactive substance expressed in days is

• 2.5

• 5

• 10

• 20

C.

10

D.

20

We know that the activity of radioactive substance

A = Ao e-λt

⇒

⇒

⇒    = ln 16

⇒    T1/2

⇒              = 9.97

⇒       T1/2 ≈ 10 days

2.

If an electron has orbital angular momentum quantum number l =7 then it will have an orbital angular momentum equal to

• $\sqrt{56}\left(\frac{\mathrm{h}}{2\mathrm{\pi }}\right)$

• $57\left(\frac{\mathrm{h}}{2\mathrm{\pi }}\right)$

• $42\left(\frac{\mathrm{h}}{2\mathrm{\pi }}\right)$

• $7\left(\frac{\mathrm{h}}{2\mathrm{\pi }}\right)$

A.

$\sqrt{56}\left(\frac{\mathrm{h}}{2\mathrm{\pi }}\right)$

$\mathrm{L}=\sqrt{\mathrm{l}\left(\mathrm{l}+1\right)}.\frac{\mathrm{h}}{2\mathrm{\pi }}=\sqrt{7×8}\frac{\mathrm{h}}{2\mathrm{\pi }}=\sqrt{56}\frac{\mathrm{h}}{2\mathrm{\pi }}$

3.

A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be

• 1840 keV

• 1/1840 keV

• 1 keV

• 920 keV

C.

1 keV

The charge on a proton is equal to e, the electronic charge.

The potential difference is V =  1kV

Kinetic Energy E = QV

= e × 103 V

E = 1 keV

Hence the kinetic energy of the proton is E = 1 KeV

4.

If the energy released in the fission of one nucleus is 3.2x10-11J, then number of nuclei required per second in a power plant of 16 kW is

• $0.5×{10}^{14}$

• $0.5×{10}^{12}$

• $5×{10}^{12}$

• $5×{10}^{14}$

D.

$5×{10}^{14}$

The number of nuclei required per second is

n=$\frac{\mathrm{P}}{\mathrm{E}}$=$\frac{16×{10}^{3}}{3.2×{10}^{-11}}=5×{10}^{14}$

5.

A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

• 16/81

• 8/9

• 8/27

• 2/3

B.

8/9

One deuteron consists of one proton and one neutron. As the mass of a proton and a neutron is approximately same ( ≈ 1.67 × 10-27 kg ), we assume that the mass of the neutron be m and the mass of the deuteron be 2mas the electron mass is negligibly small compared to that of proton and neutron.

Let the initial velocity of the neutron be u. As the deuteron is initially at rest, the final velocity of the neutron is

v1

= $-\frac{\mathrm{mu}}{3\mathrm{m}}$

v1

And the velocity of the deutron is

v2u

v2$\frac{2}{3}$u

Total energy before collision is

E1  =  $\frac{1}{2}$mu2

After the collision, the energy gained by the deuteron is

6.

A certain radioactive element has a half-life of 20 years. If we have a block with 10 g of the element in it, after how many years will there be just 2.5 g of the element in the block?

• 80 years

• 40 years

• 100 years

• 60 years

B.

40 years

T1/2 = 20 years

No = 10 g

N = 2.5 g

N = No e-λ/t

T1/2

λ = $\frac{0.693}{{\mathrm{T}}_{1}{2}}}$

⇒     e-λ/t = ln $\left(\frac{\mathrm{N}}{{\mathrm{N}}_{\mathrm{o}}}\right)$

⇒     t =

⇒         =

⇒    t =

⇒   t = 40 years

7.

Radioactive nuclei that are injected into a patient collect at certain sites within its body, undergoing radioactive decay and emitting electromagnetic radiation. These radiations can then be recorded by a detector. This procedure provides an important diagnostic tool called

• gamma camera

• CAT scan

• gamma ray spectrosccopy

C.

Radioactive nuclei that are injeted into a patient collected at certain sites within it's  body, undergoing radioactive decay and emitting electromagnetic radiation. These radiation can than be recorded by a detector. This procedure provides an important diagnostic tool called tracer technique.

8.

Reason:  Quasar has very small size

• If both the assertion and reason are true and reason is a correct explanation of the assertion.

• If both assertion and reason are true but assertion is not a correct explanation of the assertion.

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

B.

If both assertion and reason are true but assertion is not a correct explanation of the assertion.

A quasar is a very big source of radio waves and its size is very small as compared to the size of a galaxy. A radio galaxy emits radio waves which lie in the range  1030  to 1038 watt. A quasar emits radio waves which lie in the range of 1037 to 1038 watt.

9.

Mass of the proton is 1840 times that of electron. It is accelerated through a potential difference of 1V. Find its kinetic energy.

• 6 eV

• 2 eV

• 10 eV

• 1 eV

D.

1 eV

The charge on a proton = e

Hence when the proton is accelerated through a potential difference  of 1 V, its K.E = 1 eV

10.

Nuclear fusion is possible

• only between light nuclei

• only between heavy nuclei

• between both light and heavy nuclei

• only between nuclei which are stable against β-decay

A.

only between light nuclei

Nuclear fusion is possible only between light nuclei. The nuclear process of two light nuclei getting close enough to produce a larger nucleus is an energetically favourable reaction.