Half life of F 18 is 110 minutes. What fraction of F 18 sample decays in 20 minutes?

Half life of F 9 18 ( t 1 / 2 ) = 110 minutes Given time ( t ) = 20 minutes We know decay constant ( λ ) = 0 . 693 t 1 / 2 λ . t = 2 . 303 log N 0 N 0 . 693 110 × 20 = 2 . 303 log N 0 N 0 . 0547 = log N 0 N N 0 N = antilog ( 0 . 0547 ) = 1 . 134 ∴ N N 0 = 0 . 8818 N 0 - x N 0 = 0 . 8818 x N 0 = 0 · 1182 Hence, the fraction of sample decay is 0 . 1182 or 11 . 82 % .

Half life of S 35 is 87 . 8 d . What percentage of S 35 sample remains after 180 d ?

The half life of S 16 32 t 1 2 = 87 . 8 d Given time t = 180 d The decay constant λ = 0 . 693 t 1 2 = 0 . 693 87 . 8 λ . t = 2 . 303 log N ∘ N 0 . 693 87 . 8 × 180 = 2 . 303 log N ∘ N 0 . 6169 = log N ° N N ∘ N = antilog ( 0 . 6169 ) = 4 . 139 Fraction remains, N N 0 = 0 . 2416 % remains = N N ∘ × 100 = 0 . 2416 × 100 = 24 . 16 %

0 . 5 g sample of Tl 201 decays to 0 . 0788 g in 8 days. What is its half-life?

Initial mass of sample ( N o ) = 0 . 5 g Remaining mass of sample ( N ) = 0 . 0788 g Given time for decay = 8 days λt = 2 . 303 log N o N λ × 8 = 2 . 303 log 0 . 5 0 . 0788 λ = 0 . 231 Half life t 1 / 2 = 0 . 693 0 . 231 = 3 days.

65 % of In 111 sample decays in 4 . 2 d . What is its half-life?

Sample decay ( x ) = 65 % Given time ( t ) = 4 . 2 d λt = 2 . 303 log N o N o - x λ = 2 . 303 4 . 2 log 100 100 - 65 = 0 . 25 Half life ( t 1 / 2 ) = 0 . 693 λ = 0 . 693 0 . 25 t 1 / 2 = 2 . 77 d .

Calculate the binding energy per nucleon of Kr 36 84 whose atomic mass is 83 . 913 u . (Mass of neutron is that of H atom is 1 . 0078 u )

Atomic mass of Kr 36 84 ( m ) = 83 . 913 u Mass of neutron ( m n ) = 1 . 0087 u Mass of H atom ( m H ) = 1 . 0078 u Total mass = Z . m H + ( A - Z ) M n = ( 36 × 1 . 0078 ) + ( 48 × 1 . 0087 ) = 84 . 6984 u Mass defect ( ∆ m ) = Total mass - m = 84 . 6984 - 83 . 931 ∆ m = 0 . 7674 u Total binding energy = ∆ m × 931 . 4 Mev = 0 . 7674 × 931 . 4 = 714 . 756 Mev Binding energy per nucleon = Binding energy Number of nucleons = 714 . 756 84 = 8 . 5 Mev

Calculate the energy in Mev released in the nuclear reaction Ir 77 174 → Re 75 170 + He 2 4 . Atomic masses : Ir = 173 . 97 u , Re = 169 . 96 u and He = 4 . 0026 u

Ir 77 174 → Re 75 170 + He 2 4 Mass of Ir = 173 . 97 u Mass of Re = 169 . 96 u Mass of He = 4 . 0026 u Mass defect = ( mass of Ir ) - [ ( mass of Re ) + ( mass of He ) ] = 173 . 997 - 173 . 96 = 0 . 0074 u The energy released = ∆ m × 931 . 4 Mev = 0 . 0074 × 931 . 4 = 6 . 89 Mev

E M B I B E

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises

Maharashtra Board Solutions for Chapter: Nuclear Chemistry and Radioactivity, Exercise 3: Exercises

Author:Maharashtra Board

Maharashtra Board Chemistry Solutions for Exercise - Maharashtra Board Solutions for Chapter: Nuclear Chemistry and Radioactivity, Exercise 3: Exercises

Attempt the practice questions on Chapter 13: Nuclear Chemistry and Radioactivity, Exercise 3: Exercises with hints and solutions to strengthen your understanding. Chemistry solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Nuclear Chemistry and Radioactivity, Exercise 3: Exercises with Hints & Solutions

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

Half life of $∴ \frac{N}{N_{0}} = 0.8818$ is $110$ minutes. What fraction of ${}^{18}F$ sample decays in $20$ minutes?

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

Half life of ${}^{35}S$ is $87.8 d$ . What percentage of ${}^{35}S$ sample remains after $180 d$ ?

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

Half life of $^{67} Ga$ is $78 h$ . How long will it take to decay $12 %$ of sample of $Ga$ ?

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

$0.5 g$ sample of ${}^{201}{Tl}$ decays to $0.0788 g$ in $8$ days. What is its half-life?

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

$65 %$ of ${}^{111}{In}$ sample decays in $4.2 d$ . What is its half-life?

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

Calculate the binding energy per nucleon of ${}_{36}^{84}{Kr}$ whose atomic mass is $83.913 u$ . (Mass of neutron is that of $H$ atom is $1.0078 u)$

HARD

11th Maharashtra Board

IMPORTANT

Chemistry>Chapter 13 - Nuclear Chemistry and Radioactivity>Exercises>Q 4

Calculate the energy in $Mev$ released in the nuclear reaction ${}_{77}^{174}{Ir} \to {}_{75}^{170}{Re} + {}_{2}^{4}{He}$ . Atomic masses $: Ir = 173.97 u,$ $Re = 169.96 u$ and $He = 4.0026 u$