Home
Class 12
PHYSICS
A sample contains 10^(-2)kg each of two ...

A sample contains `10^(-2)kg` each of two substances A and B with half lives 4 sec and 8 sec respectively. Their atomic weights are in the ratio `1:2`. Find the amounts of A and B after an interval of 16 seconds.

A

`A = 0.625 xx 10^(-4) kg, B = 0.25 xx 10^(-3) kg`

B

`A = 0.25 xx 10^(-3) kg, B = 0.625 xx 10^(-4) kg`

C

`A = 2.5 xx 10^(-3) kg, B = 6.25 xx 10^(-4) kg`

D

`A = 6.25 xx 10^(-3) kg, B = 2.5 xx 10^(-3) kg`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to calculate the remaining amounts of substances A and B after 16 seconds, given their half-lives and initial masses. ### Step-by-Step Solution: 1. **Identify Initial Conditions**: - Initial mass of substance A, \( m_{A0} = 10^{-2} \, \text{kg} \) - Initial mass of substance B, \( m_{B0} = 10^{-2} \, \text{kg} \) - Half-life of substance A, \( t_{1/2A} = 4 \, \text{sec} \) - Half-life of substance B, \( t_{1/2B} = 8 \, \text{sec} \) 2. **Calculate the Number of Half-Lives**: - For substance A: \[ \text{Number of half-lives for A} = \frac{\text{Total time}}{t_{1/2A}} = \frac{16 \, \text{sec}}{4 \, \text{sec}} = 4 \] - For substance B: \[ \text{Number of half-lives for B} = \frac{\text{Total time}}{t_{1/2B}} = \frac{16 \, \text{sec}}{8 \, \text{sec}} = 2 \] 3. **Calculate Remaining Mass of Substance A**: - The formula for the remaining mass after \( n \) half-lives is: \[ m_A = m_{A0} \left( \frac{1}{2} \right)^{n_A} \] - Substituting the values: \[ m_A = 10^{-2} \left( \frac{1}{2} \right)^{4} = 10^{-2} \cdot \frac{1}{16} = \frac{10^{-2}}{16} = 6.25 \times 10^{-4} \, \text{kg} \] 4. **Calculate Remaining Mass of Substance B**: - Using the same formula: \[ m_B = m_{B0} \left( \frac{1}{2} \right)^{n_B} \] - Substituting the values: \[ m_B = 10^{-2} \left( \frac{1}{2} \right)^{2} = 10^{-2} \cdot \frac{1}{4} = \frac{10^{-2}}{4} = 2.5 \times 10^{-3} \, \text{kg} \] 5. **Final Result**: - The remaining mass of substance A after 16 seconds is \( 6.25 \times 10^{-4} \, \text{kg} \). - The remaining mass of substance B after 16 seconds is \( 2.5 \times 10^{-3} \, \text{kg} \). ### Summary: - Mass of A after 16 seconds: \( 6.25 \times 10^{-4} \, \text{kg} \) - Mass of B after 16 seconds: \( 2.5 \times 10^{-3} \, \text{kg} \)
Promotional Banner

Similar Questions

Explore conceptually related problems

Two bulbs A and B contains 16 g O_(2) and 16 g O_(3) , respectively. Which of the statements are ture?

The number of nuclei of two radioactive substance is the same and their half-lives are 1 year and 2 years respectively. The ratio of their activities after 6 years will be

A sample of radioactive material decays simultaneouly by two processes A and B with half-lives (1)/(2) and (1)/(4)h , respectively. For the first half hour it decays with the process A, next one hour with the proecess B, and for further half an hour with both A and B. If, origianlly, there were N_0 nuceli, find the number of nuclei after 2 h of such decay.

A sample of radioactive material decays simultaneouly by two processes A and B with half-lives (1)/(2) and (1)/(4)h , respectively. For the first half hour it decays with the process A, next one hour with the proecess B, and for further half an hour with both A and B. If, origianlly, there were N_0 nuceli, find the number of nuclei after 2 h of such decay.

Two radioactive substances X and Y initially contain an equal number of atoms. Their half-lives are 1 hour and 2 hours respectively. Then the ratio of their rates of disintergration after two hours is

Two radioactive substances X and Y initially contain equal number of atoms. Their half-lives are 1 hour and 2 hours respectively. Calculate the ratio of their rates of disintegration after four hours.

Two particles A and B of mass 1 kg and 4 kg respectively approach each other due to their mutual gravitational force only. Then the ratio of acceleration of A to B at any instant is

Two trains running in opposite directions to each other, cross a man standing on the platform in 30 sec and 12 sec respectively and they cross each other in 20 seconds. Find the ratio of their speed.

The half-lives of radio isotypes P^32 and P^33 are 14 days and 28 days respectively. These radioisotopes are mixed in the ratio of 4:1 of their atoms. It the initial activity of the mixed sample is 3.0 mCi, find the activity of the mixed isotopes after 60 years.

At any instant, the ratio of the amounts of two radioactive substance is 2:1 . If their half-lives be, respectively, 12h and 16h , then after two days, what will be the ratio of the substances?