Question

The fraction of atoms of radioactive element that decays in 6 days is 7/8. The fraction that decays in 10 days will be-

• A. 70/80
• B. 77/88
• C. 31/32
• D. 35/36

Answer 1

Answer: (C)

31/32

Answer 2

$\frac { \mathrm { N } } { \mathrm { N } _ { 0 } } = \frac { 1 } { 8 } = \left( \frac { 1 } { 2 } \right) ^ { 3 } = \left( \frac { 1 } { 2 } \right) ^ { \frac { 6 } { \mathrm {~T} } } \Rightarrow \mathrm {~T} = \frac { 6 } { 3 } = 2$ daysso, $\frac { \mathrm { N } ^ { \prime } } { \mathrm { N } _ { 0 } } = \left( \frac { 1 } { 2 } \right) ^ { \frac { 10 } { 2 } } = \left( \frac { 1 } { 2 } \right) ^ { 5 } \frac { 1 } { 32 }$ $\Rightarrow \frac { \mathrm {~N} _ { \mathrm { s } } } { \mathrm { N } _ { 0 } } = 1 - \frac { \mathrm { N } ^ { \prime } } { \mathrm { N } _ { 0 } } = 1 - \frac { 1 } { 32 } = \frac { 31 } { 32 }$