Atoms and Nuclei — Page 9 | NEET Physics

Q81

Two radioactive substances A and B have decay constants 5

\lambda

and

\lambda

respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e) 2 after a time interval

A

4\lambda

B

2\lambda

C 1/

2\lambda

D 1/

4\lambda

Correct Answer

Option C

Solution

N A = N 0 e –5 $\lambda$ t N B = N 0 e – $\lambda$ t Given

{{{N_A}} \over {{N_B}}}

=

{\left( {{1 \over e}} \right)^2}

$\Rightarrow$

{{{N_0}{e^{ - 5\lambda t}}} \over {{N_0}{e^{ - \lambda t}}}}

=

{\left( {{1 \over e}} \right)^2}

$\Rightarrow$ e –4 $\lambda$ t = e -2 $\Rightarrow$ t =

{1 \over {2\lambda }}

Q82

The radius of germanium (Ge) nuclide is measured to be twice the radius of

{}_4^9

Be. The number of nucleons in Ge are

A 72

B 73

C 74

D 75

Correct Answer

Option A

Solution

For berillium, R 1 = R 0 (9) 1/3 For germanium, R 2 = R 0 A 1/3

{{{R_1}} \over {{R_2}}}

=

{{{{\left( 9 \right)}^{1/3}}} \over {{A^{1/3}}}}

$\Rightarrow$

{1 \over 2}

=

{{{{\left( 9 \right)}^{1/3}}} \over {{A^{1/3}}}}

$\Rightarrow$

{1 \over 8} = {9 \over A}

$\Rightarrow$ A = 72

Q83

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emited by hydrogen will be

A one

B two

C three

D four

Correct Answer

Option C

Solution

Energy required for exciting the hydrogen atom in the ground state to orbit n is given by E = E n - E 1 $\Rightarrow$ 12.1 =

- {{13.6} \over {{n^2}}}

-

\left( { - {{13.6} \over {{1^2}}}} \right)

= 3 $\Rightarrow$ n 2 =

{{{13.6} \over {1.5}}}

= 9 $\Rightarrow$ n = 3 Number of spectral lines emitted =

{{n\left( {n - 1} \right)} \over 2}

=

{{3 \times 2} \over 2}

Q84

In a radioactive material the activity at time t 1 is R 1 and at a later time t 2 , it is R 2 . If the decay constant of the material is

\lambda

, then

A R 1 = R 2

B R 1 = R 2 e

-

\lambda

(t 1

-

t 2 )

C R 1 = R 2 e

\lambda

(t 1

-

t 2 )

D R 1 = R 2 (t 2 /t 1 ).

Correct Answer

Option B

Solution

R 1 = R 0 e - $\lambda$ t 1 and R 2 = R 0 e - $\lambda$ t 2 $\therefore$

{{{R_1}} \over {{R_2}}}

=

{{{R_0}{e^{ - \lambda {t_1}}}} \over {{R_0}{e^{ - \lambda {t_2}}}}}

=

{{e^{ - \lambda \left( {{t_1} - {t_2}} \right)}}}

$\Rightarrow$ R 1 = R 2 e $-$ $\lambda$ (t 1 $-$ t 2 )

Q85

The binding energy of deuteron is 2.2 MeV and that of

{}_2^4

He is 28 MeV. If two deuterons are fused to form one

{}_2^4

He then the energy released is

A 30.2 MeV

B 25.8 MeV

C 23.6 MeV

D 19.2 MeV

Correct Answer

Option C

Solution

{}_1^2H

+

{}_1^2H

$\to$

{}_2^4He

+ energy Energy released = 28 – 2 × 2.2 = 23.6 MeV

Q86

Energy levels A, B and C of a certain atom corresponding to increasing values of energy i.e. E A < E B < E C . If

\lambda

1 ,

\lambda

2 and

\lambda

3 are wavelengths of radioations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct?

A

{\lambda _3} = {\lambda _1} + {\lambda _2}

B

{\lambda _3} = {{{\lambda _1}{\lambda _2}} \over {{\lambda _1} + {\lambda _2}}}

C

{\lambda _1} + {\lambda _2} + {\lambda _3} = 0

D

{\lambda _3}^2 = {\lambda _1}^2 + {\lambda _2}^2

Correct Answer

Option B

Solution

$\therefore$ (E C – E B ) + (E B – E A ) = (E C – E A ) $\Rightarrow$

{{hc} \over {{\lambda _3}}} = {{hc} \over {{\lambda _1}}} + {{hc} \over {{\lambda _2}}}

$\Rightarrow$

{\lambda _3} = {{{\lambda _1}{\lambda _2}} \over {{\lambda _1} + {\lambda _2}}}

Q87

Fission of nuclei is possible because the binding energy per nucleon in them

A increases with mass number at low mass numbers

B decreases with mass number at low mass numbers

C increases with mass number at high mass numbers

D decreases with mass number at high mass numbers.

Correct Answer

Option D

Solution

For nuclei having A $>$ 56 binding energy per nucleon gradually decreases.

Q88

In any fission process the ratio mass of fission products mass of parent nucleus is

A equal to 1

B greater than 1

C less than 1

D depends on the mass of the parent nucleus.

Correct Answer

Option C

Solution

Binding energy per nucleon for fission products is higher relative to Binding energy per nucleon for parent nucleus, i.e., more masses are lost and are obtained as kinetic energy of fission products.

So, the given ratio $<$ 1.

Q89

Which one of the following pairs of nuclei are isotones ?

A 34 Se 74 , 31 Ga 71

B 38 Sr 84 , 38 Sr 86

C 42 Mo 92 , 40 Zr 92

D 20 Ca 40 , 16 S 32

Correct Answer

Option A

Solution

Isotones means number of neutron remains same.

Q90

The total energy of an electron in the first excited state of hydrogen atom is about

-

3.4 eV. Its kinetic energy in this state is

A 3.4 eV

B 6.8 eV

C

-

3.4 eV

D

-

6.8 eV

Correct Answer

Option A

Solution

Apply Bohr's Atomic model for H-atom K.E = -T.E = +3.4 eV