Calculate the nuclear radii of Ba 8 140 and O 8 17 . Given R 0 = 1 . 5 fm .

Given, R 0 = 1 . 5 fm The mass number of B 8 140 a is A 1 = 140 The mass number of O 8 17 is A 2 = 17 We know that the radius is given as, R = R 0 A 1 3 , where A is the mass number. Therefore, the radius of Barium becomes, R 1 = R 0 ( A 1 ) 1 / 3 = R 0 ( 140 ) 1 / 3 = 1 . 5 × 5 . 2 = 7 . 8 fm Similarly, the radius of Oxygen becomes, R 2 = R 0 ( A 2 ) 1 / 3 = R 0 ( 17 ) 1 / 3 = 1 . 5 × 2 . 57 = 3 . 85 fm

Calculate the nuclear radii of Ba 8 140 and O 8 17 . Given R 0 = 1 . 5 fm .

Given, R 0 = 1 . 5 fm The mass number of B 8 140 a is A 1 = 140 The mass number of O 8 17 is A 2 = 17 We know that the radius is given as, R = R 0 A 1 3 , where A is the mass number. Therefore, the radius of Barium becomes, R 1 = R 0 ( A 1 ) 1 / 3 = R 0 ( 140 ) 1 / 3 = 1 . 5 × 5 . 2 = 7 . 8 fm Similarly, the radius of Oxygen becomes, R 2 = R 0 ( A 2 ) 1 / 3 = R 0 ( 17 ) 1 / 3 = 1 . 5 × 2 . 57 = 3 . 85 fm

Find nuclear mass density of U 92 238 . Given R 0 = 1 . 5 fm and mass of each nucleon = 1 . 67 × 10 - 27 kg . .

Given, R 0 = 1 . 5 fm Mass per nucleon, M = 1 . 67 × 10 - 27 kg The mass number, A = 238 Density = Mass Volume ⇒ d = A × M A × 4 3 π R 0 3 = 238 × 1.66 × 10 − 27 238 × 4 3 π × ( 1.5 × 10 − 15 ) 3 = 1 .18 × 10 17 kg / m 3

Calculate the binding energy per nucleon for a C 6 12 nucleus. Atomic mass of C 6 12 = 12 amu , mass of a proton = 1 . 007825 amu , mass of a neutron = 1 . 008665 amu .

Given, The mass of proton is m p = 1 . 007825 amu The mass of neutron, m n = 1 . 008665 amu The mass of the atom is, m = 12 amu By neglecting the mass of electrons, the mass of the nucleus of the carbon atom can be approximated to m = 12 amu . Mass number of Carbon is, A = 12 Carbon has 6 protons and 6 neutrons. The difference in mass of the nucleus and the nucleons is, ∆ m = expected mass - ( actual mass ) ⇒ Δ m = 6 m p + 6 m n - m ⇒ Δ m = 6 ( 1 . 007825 + 1 . 008665 ) - 12 = 0 . 09894 amu The mass energy equivalent of 1 amu is 931 MeV . Hence, the binding energy is, B E = 0 . 09894 × 931 MeV = 92 . 113 MeV Binding energy per nucleon is, B E ¯ = B E A = 92 . 113 12 MeV = 7 . 68 MeV

E M B I B E

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 8

MEDIUM

12th CBSE

IMPORTANT

Earn 100

Calculate the nuclear radii of ${}_{8}^{140}{Ba}$ and ${}_{8}^{17}O$ . Given $R_{0} = 1.5 fm .$

Important Questions on Nuclei

EASY

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 9

The nuclear radius of

{Pb}^{208}

is

8.874 fm .

What will be the nuclear radius of

{Ca}^{44} ?

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 10

A nucleus with

A = 235

splits into two nuclei whose mass numbers are in the ratio

2 : 1

. If

R_{0} = 1.4 fm

, find the radii of the new nuclei.

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 11

Calculate the density of hydrogen nucleus in

SI

units. Given

R_{0} = 1.1 fm

and

m_{p} = 1.007825 amu

. Take,

1 amu = 1.66054 \times 10^{- 27} kg

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 12

The nuclear radius of

{}_{8}^{16}O

is

3 \times 10^{- 15} m .

Find the density of nuclear matter. Take, the mass of proton and neutron to be,

m = 1.67 \times 10^{- 27} kg

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 13

Find nuclear mass density of

{}_{92}^{238}U

. Given

R_{0} = 1.5 fm

and mass of each nucleon

= 1.67 \times 10^{- 27} kg .

.

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 1

The mass of

{}_{3}^{7}{Li}

is

0.042 amu

less than the sum of masses of its nucleons. Find the

B . E .

per nucleon. Take,

1 amu = 931.5 MeV / c^{2}

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 2

Calculate the binding energy per nucleon for a

{}_{6}^{12}C

nucleus. Atomic mass of

{}_{6}^{12}C = 12 amu

, mass of a proton

= 1.007825 amu

, mass of a neutron

= 1.008665 amu

.

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 5 - Nuclei>Problems For Practice>Q 3

Calculate the binding energy of a deuteron. Given that
mass of proton $= 1.007825 amu$
mass of a neutron $= 1.008665 amu$
mass of a deuteron $= 2.014103 amu$