The nuclide C 14 contains (a) how many protons and (b) how many neutrons?

For C 14 6 , the atomic number is same as the number of protons, Z = 6 . The number of neutrons is the difference between atomic mass and atomic number = A - Z = 14 - 6 = 8 .

The nuclide C 14 contains (a) how many protons and (b) how many neutrons?

For C 14 6 , the atomic number is same as the number of protons, Z = 6 . The number of neutrons is the difference between atomic mass and atomic number = A - Z = 14 - 6 = 8 .

The half-life of a particular radioactive isotope is 6 . 5 h . If there are initially 65 × 10 19 atoms of this isotope, how many remain at the end of 26 h ?

Given: Half-life, T = 6 .5 h Age of the sample, t = 26 h Initial number of atoms, N 0 = 65 × 10 19 ∴ Number of half-lives, n = t T = 26 6 .5 = 4 Number of atoms remaining in terms of number of half-lives, N = N 0 2 n = 65 × 10 19 2 4 = 406 .25 × 10 17

Consider the three formation processes shown for the compound nucleus Ne 20 in the figure below. Here are some of the atomic and particle masses: Ne 20 19 . 992 44 u α 4 . 002 60 u F 19 18 . 998 40 u p 1 . 007 83 u O 16 15 . 994 91 u What energy must (a) the alpha particle, (b) the proton and (c) the γ -ray photon have to provide 25 . 0 MeV of excitation energy to the compound nucleus?

Given, the atomic mass of each nuclei, Ne 20 = 19 . 992 u , F 19 = 18 . 99840 u O 16 = 15 . 99491 u , α = 4 . 00260 u P = 1 . 00783 u . A general nucleus formation reaction is given by, A + a → B , where, A is the target nucleus, a is the incident light particle and B is the excited compound nucleus ( Ne 20 ) . Let us assume that A is at rest initially. According to the conservation of energy, m A c 2 + m a c 2 + k a = m B c 2 + k B + E B . . . 1 Here, m A , m a and m B are the masses, k a and k B are kinetic energies of a and B , E B is the excitation energy of B and c is the speed of light. According to the linear momentum principle, P a = P B , where P a and P B are the linear momenta. ∵ P a = P B . So, k B = P B 2 2 m B , k a = P a 2 2 m a P a 2 = 2 m a k a . . . ( 2 ) ∴ Therefore, k B = P B 2 2 m B = P a 2 2 m B = m a m B k a ∴ k B = m a m B k a . . . 3 On putting the value of k B in equation 1 , ∴ m A c 2 + m a c 2 + k a = m B c 2 + m a m B k a + E B ∴ k a 1 - m a m B = m B - m A - m a c 2 + E B . Therefore, k a = m B m B - m a m B - m A - m a c 2 + E B . (a) Let A represent the Oxygen nucleus O 16 and a represent the α particle. O 16 + α → Ne 20 On comparing this with equation 1 , A + a → B ∴ k α = m Ne m Ne - m α m Ne - m o - m α c 2 + E Ne ∴ m Ne - m o - m α c 2 = ( 19 . 99244 - 15 . 99491 - 4 . 00260 ) × 991 . 5 MeV = - 4 . 723 MeV . ∴ E Ne = 25 MeV ∴ k α = 19 . 99244 19 . 99244 - 4 . 00260 ( - 4 . 723 + 25 ) MeV k α = 1 . 25 × 20 . 277 MeV = 25 . 35 MeV . So, k α = 25 . 35 MeV . (b) Let A represent F 19 nucleus and a represent the proton p . Then, F 19 + P → 20 Ne On comparing with equation 1 , A + a → B . So, k p = m Ne m Ne - m p m Ne - m p - m F c 2 + E Ne ∴ m Ne - m p - m F c 2 = ( 19 . 99244 - 18 . 99840 - 1 . 00783 ) × 931 . 5 MeV = - 12 . 845 MeV . So, k p = 19 . 99244 19 . 99244 - 1 . 00783 × ( - 12 . 845 + 25 ) k p = 12 . 80 MeV . (c) Let A represent the Ne 20 nucleus and a represent γ photon. So, [ Ne 20 + y → Ne 20 ] . As we know that the rest mass of photon is zero, we need to conserve the energy where E γ represents energy of γ photon. So, according to energy conservation, m Ne c 2 + E γ = m Ne c 2 + k Ne + E Ne . So, E γ = k Ne + E Ne . . . 4 ∴ We can relate the photon energy and momentum as, P γ = E γ c , where P γ is the momentum of γ photon, E γ is the energy of γ photon and c is the speed of light. ∴ Kinetic energy k Ne is given by, k Ne = P Ne 2 2 m Ne = P γ 2 2 m Ne = E γ 2 2 m Ne c 2 ∴ P Ne = P γ . On substituting the value of k Ne in equation 4 , E γ = E γ 2 2 m Ne c 2 + E Ne . It is a quadratic equation in E γ , E γ = E γ 2 2 m Ne c 2 + E Ne E γ 2 - 2 m Ne c 2 E γ + 2 m Ne c 2 E Ne = 0 E γ = 2 m Ne c 2 E γ ± 2 m Ne c 2 2 - 4 × 1 × 2 m Ne c 2 E Ne 2 . So, E γ = m Ne c 2 ± m Ne c 2 2 - 2 m Ne c 2 E Ne . Since we use the relativistic concept between energy and momentum of Ne 20 nucleus, only one solution would be obtained, i.e., E γ = m Ne c 2 - m Ne c 2 2 - 2 m Ne c 2 E Ne . So, m Ne c 2 = ( 19 . 99244 ) × 931 . 5 MeV = 18622 MeV = 1 . 8622 × 10 4 MeV . So, E γ = 1 . 8622 × 10 4 - 1 . 8622 × 10 4 2 - 2 1 . 8622 × 10 4 × ( 25 ) E γ = 1 . 8622 × 10 4 - 1 . 8597 × 10 4 MeV E γ = 25 MeV . So, we can calculate k Ne as, k Ne = E γ 2 2 m Ne c 2 = ( 25 ) 2 2 × 1 . 8622 × 104 k Ne = 0 . 01678 MeV . Since the value of k Ne is very less compared to E γ = 25 MeV , so, all the photon energy is utilised for excitation of the nucleus.

Calculate the mass of a sample of (initially pure) K 40 that has an initial decay rate of 6 . 20 × 10 5 disintegrations s - 1 . The isotope has a half-life of 1 . 28 × 10 9 y .

Given: Decay rate, d N d t = 6 .20 × 10 5 disintegrations s - 1 Half-life, T = 1 .28 × 10 9 y = 1 .28 × 10 9 × 365 × 24 × 60 × 60 s = 4036608 × 10 10 s Mass of the given sample = ? Decay rate, d N d t = λ Ν = ln 2 T × m M × N A where, M is molecular mass and N A is Avogadro's number. ⇒ 6 .2 × 10 5 = 0 .693 4036608 × 10 10 × m 40 × 6 .023 × 10 23 ⇒ m ≃ 2 .4 g

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IMPORTANT

Earn 100

The nuclide ${}^{14}C$ contains (a) how many protons and (b) how many neutrons?

Important Questions on Nuclear Physics

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JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 1

U^{238}

nucleus emits a

4.196 MeV

alpha particle. Calculate the disintegration energy

Q

for this process, taking the recoil energy of the residual

{Th}^{234}

nucleus into account.

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 2

The half-life of a particular radioactive isotope is

6.5 h

. If there are initially

65 \times 10^{19}

atoms of this isotope, how many remain at the end of

26 h

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 3

Consider the three formation processes shown for the compound nucleus ${}^{20}{Ne}$ in the figure below. Here are some of the atomic and particle masses:

Question Image

${}^{20}{Ne}$	$19.992 44 u$	$α$	$4.002 60 u$
${}^{19}F$	$18.998 40 u$	$p$	$1.007 83 u$
${}^{16}O$	$15.994 91 u$

What energy must (a) the alpha particle, (b) the proton and (c) the $γ$ -ray photon have to provide $25.0 MeV$ of excitation energy to the compound nucleus?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 4

Plutonium isotope

{Pu}^{239}

decays by alpha decay, with a half-life of

24100 y

. How many

milligrams

of helium is produced by an initially pure

10.0 g

sample of

{Pu}^{239}

at the end of

20000 y

?
(Consider only the helium produced directly by plutonium and not by any by-products of the decay process)

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 5

An organic sample of mass

4.00 kg

absorbs

2.00 mJ

via slow neutron radiation (RBE

= 5

). What is the dose equivalent

(mSv)

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 6

Calculate the mass of a sample of (initially pure)

K^{40}

that has an initial decay rate of

6.20 \times 10^{5} disintegrations s^{- 1}

. The isotope has a half-life of

1.28 \times 10^{9} y

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 7

The nuclide

{Au}^{198}

, with a half-life of

2.70 d

is used in cancer therapy. What mass of this nuclide is required to produce an activity of

250 Ci

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 38 - Nuclear Physics>Problems>Q 8

What is the activity of a

10 ng

sample of

{Kr}^{92}

, which has a half-life of

1.84 s

The nuclide C14 contains (a) how many protons and (b) how many neutrons?

Important Questions on Nuclear Physics

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The nuclide ${}^{14}C$ contains (a) how many protons and (b) how many neutrons?