# IB DP Physics E.3 Radioactive decay IB Style Question Bank HL Paper 1

### Question

Radioactive nuclide $$X$$ decays into a stable nuclide $$Y$$. The decay constant of $$X$$ is $$\lambda$$. The variation with time $$t$$ of number of nuclei of $$X$$ and $$Y$$ are shown on the same axes.

What is the expression for $$s$$ ?
A. $$\frac{\ln 2}{\lambda}$$

B. $$\frac{1}{\lambda}$$

C. $$\frac{\lambda}{\ln 2}$$

D. $$\ln 2$$

Ans:A

Certainly! In the context of radioactive decay, the parameter $$s$$ represents the half-life of a radioactive substance. The half-life is the amount of time it takes for half of a sample of radioactive nuclei to decay into a stable product. It’s a fundamental concept in nuclear physics and is a measure of how quickly a radioactive substance decays.

The half-life ($$s$$) is related to the decay constant ($$\lambda$$) as follows:

$s = \frac{\ln 2}{\lambda}$

Where:

•  $$s$$ is the half-life of the radioactive substance.
• $$\lambda$$ is the decay constant of the substance.
• $$\ln 2$$ is the natural logarithm of 2.

### Question

A student measures the count rate of a radioactive sample with time in a laboratory. The background count in the laboratory is 30 counts per second.

What is the time at which the student measures a count rate of 45 counts per second?

A. $$30 \mathrm{~s}$$

B. $$40 \mathrm{~s}$$

C. $$60 \mathrm{~s}$$

D. $$80 \mathrm{~s}$$

Ans:C

Background count rate is 30 , so count rate at t=0 is 120 and at t=20 will be 60 .

From this conclusion clearly we can see half life is 20 sec (time required to half of initial value).

$t_{1/2}=20 ~sec$

$$120\underset{t_{1/2}} \longrightarrow 60\underset{t_{1/2}} \longrightarrow 30 \underset{t_{1/2}}{\longrightarrow} 15$$

As background count rate will always present , when count rate will be 15 due to background count rate addition of 30 it will become 45.

Total time $3\times t_{1/2}\Rightarrow 3\times 20 = 60 \mathrm{~s}$

### Question

Nuclide X can decay by two routes. In Route 1 alpha (α) decay is followed by beta-minus ((β– decay. In Route 2 β decay is followed by α decay. P and R are the intermediate products and Q and S are the final products.

Which statement is correct?

A Q and S are different isotopes of the same element.

B The mass numbers of X and R are the same.

C The atomic numbers of P and R are the same.

D X and R are different isotopes of the same element.

Route 1:

$$X\overset{\alpha }{\rightarrow}P\overset{\beta ^{-}}{\rightarrow}Q$$

$$^{A}_{Z}X\rightarrow ^{A-4}_{Z-2}X{}’\rightarrow ^{A-4}_{Z-1}X{}”$$

Route 2:

$$X\overset{\beta ^{-} }{\rightarrow}R\overset{\alpha }{\rightarrow}\delta$$

$$^{A}_{Z}X\overset{\beta ^{-}}{\rightarrow}^{A}_{Z-1}X{}”\overset{\alpha }{\rightarrow}^{A-4}_{Z-3}X{}”$$

Question

The graph shows the variation with time t of the activity A of a radioactive sample. The energy released in each decay is E. The shaded area is equal to S.

What does the quantity S $$\times$$ E represent?

A. Average energy produced in 2 s.
B. Average power produced in 2 s.
C. Total energy produced in 2 s.
D. Maximum power produced in 2 s.

### Markscheme

C

Question

$$_{\;{\text{6}}}^{{\text{11}}}{\text{C}}$$ undergoes $${\beta ^ + }$$ decay. The products of this decay are the $${\beta ^ + }$$ particle, X and Y. What are X and Y?