A particular rock is thought to be 280 million years old. If it contains 3 . 70 mg of U 238 , how much Pb 206 should it contain?

Molar masses, M U = 238 u and M Pb = 206 u Mass of uranium, m U = 3 .7 mg Mass of lead, m Pb = ? Initial mass of uranium, m 0 = m U + m Pb Age of the rock, t = 280 × 10 6 y Half-life of uranium, T = 4 .47 × 10 9 y Initial number of uranium nuclei in the rock is, m 0 m U = m U M U + m Pb M Pb 3 .7 + m Pb 238 = 3 .7 238 + m Pb 206 ⇒ 1 − 3 .7 238 = m Pb 206 − m Pb 238 ⇒ 238 − 3 .7 238 − m Pb 238 − 206 206 × 238 ⇒ m Pb = 1508 mg

What is the binding energy per nucleon of the americium isotope Am 95 244 ? Here are some atomic masses and the neutron mass: Am 95 244 = 244 . 064 279 u , H 1 = 1 . 007 825 u and n = 1 . 008 665 u .

The atomic mass of A m 244 is, m Am = 244 .064279 u , the atomic mass of H 1 is, m H = 1 .007825 u , the mass of neutron is, m n = 1 .008665 u , the atomic number of Am is, Z = 95 , the number of neutrons, A − Z = 244 − 95 = 149 . Binding energy in terms of atomic masses and neutron mass is, B E = [ Z × m H + A − Z m n ] − m Am × 931 .5 = 95 × 1 .007825 + 149 × 1 .008665 − 244 .064279 × 931 .5 = 1 .97081 × 931 .5 = 1835 .22 MeV . Binding energy per nucleon = Binding energy Mass number = B E A = 1835 .22 244 = 7 .7514 MeV .

Verify the binding energy per nucleon for the Plutonium isotope Pu 239 . The mass of the neutral atom is 239 . 052 16 u .

The atomic mass of Pu 239 is, m Pu = 239 .05216 u , the atomic mass of H is, m H = 1 .007825 u , the mass of neutron is, m n = 1 .008665 u , the atomic number of Pu is, Z = 94 , the number of neutrons = A - Z = 239 - 94 = 145 . Binding energy in terms of atomic masses and neutron mass is, B E = Z × m H + A − Z m n − m A m × 931 .5 MeV = 94 × 1 .007825 + 145 × 1 .008665 − 239 .05216 × 931 .5 = 1 . 939815 × 931 . 5 = 1806 . 94 MeV . Binding energy per nucleon = B E A = 1806 .94 239 = 7 .56 MeV .

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IMPORTANT

Earn 100

What is the binding energy per nucleon of the europium isotope ${Eu}_{63}^{152}$ ? Here are some atomic masses and the neutron mass.
${Eu}_{63}^{152} = 151.921 742 u$ , $H^{1} = 1.007 825 u$ and $n = 1.008 665 u$ .

Important Questions on Nuclear Physics

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 39

The radionuclide

P^{32}

decays to

S^{32}

as described by

P^{32} \to S^{32} + e^{-} + \bar{γ} + Q

. In a particular decay event, a

1.71 MeV

electron is emitted, the maximum possible value. What is the kinetic energy of the recoiling

S^{32}

atom in this event? (Hint: For the electron, it is necessary to use the relativistic expressions for kinetic energy and linear momentum. The,

S^{32}

atom is non-relativistic).

EASY

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IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 40

What is the mass excess

∆_{1}

H^{1}

(actual mass is

1.007 825 u

) in (a) atomic mass units and (b)

MeV c^{- 2}

? What is the mass excess

∆_{n}

of a neutron (actual mass is

1.008 665 u

) in (c) atomic mass units and (d)

MeV c^{- 2}

? What is the mass excess

∆_{120}

{Sn}^{120}

(actual mass is

119.902 197 u

) in (e) atomic mass units and (f)

MeV c^{- 2}

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IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 41

{Li}^{7}

nucleus with a kinetic energy of

3.00 MeV

is sent towards a

{Th}^{232}

nucleus. What is the least centre-to-centre separation between the two nuclei, assuming that the (more massive)

{}^{232}{Th}

nucleus does not move?

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IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 42

A particular rock is thought to be

280

million years old. If it contains

3.70 mg

U^{238}

, how much

{Pb}^{206}

should it contain?

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 43

A radioactive nuclide has a half-life of

30.0 y

. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of (a)

60.0 y

and (b)

90.0 y

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IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 44

What is the binding energy per nucleon of the americium isotope ${}_{95}^{244}{Am}$ ? Here are some atomic masses and the neutron mass:

${}_{95}^{244}{Am} = 244.064 279 u$ , ${}^{1}H = 1.007 825 u$ and $n = 1.008 665 u$ .

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IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 45

Verify the binding energy per nucleon for the Plutonium isotope

{}^{239}{Pu}

. The mass of the neutral atom is

239.052 16 u

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IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 46

A penny has a mass of

2.8 g

. Calculate the energy that would be required to separate all the neutrons and protons in this coin from one another. For simplicity, assume that the penny is made entirely of

{}^{63}{Cu}

atoms (of mass

62.929 60 u

). The masses of the proton-plus-electron and neutron are

1.007 83 u

and

1.008 66 u

, respectively,

What is the binding energy per nucleon of the europium isotope Eu63152? Here are some atomic masses and the neutron mass. Eu63152=151.921 742 u, H1=1.007 825 u and n=1.008 665 u.

Important Questions on Nuclear Physics

Learn and Prepare for any exam you want !

What is the binding energy per nucleon of the europium isotope ${Eu}_{63}^{152}$ ? Here are some atomic masses and the neutron mass.
${Eu}_{63}^{152} = 151.921 742 u$ , $H^{1} = 1.007 825 u$ and $n = 1.008 665 u$ .