A sample contains an isotope of half-life t 1 2 .Calculate the fraction $f$ after each of the following times t 1 2 .

The quantity f is the ratio of atoms remaining to decay to the original number of atoms in the sample given by f = N N 0 . When t = t 1 2 , we have f = 1 2 = e - λ t 1 2 Taking logarithms of both sides, ln 1 2 = - λ t 1 2 Therefore, we have λ = - ln 1 2 t 1 2 . Then the equation f = e - λ t becomes f = e ln 1 2 t t 1 2 . Thus, f = 1 2 t t 1 2 Hence, fraction f after time t 1 2 is f = 1 2 t 1 2 t 1 2 = 0 . 5

A sample contains an isotope of half-life t 1 2 .Calculate the fraction $f$ after each of the following times 2 t 1 2 .

The quantity f is the ratio of atoms remaining to decay to the original number of atoms in the sample given by f = N N 0 . When t = t 1 2 , we have f = 1 2 = e - λ t 1 2 Taking logarithms of both sides, ln 1 2 = - λ t 1 2 Therefore, we have λ = - ln 1 2 t 1 2 . Then the equation f = e - λ t becomes f = e ln 1 2 t t 1 2 . Thus, f = 1 2 t t 1 2 Hence, fraction f after time 2 t 1 2 is f = 1 2 t 1 2 2 t 1 2 = 0 . 25

A sample contains an isotope of half-life t 1 2 .Calculate the fraction $f$ after each of the following times 2 . 5 t 1 2 .

The quantity f is the ratio of atoms remaining to decay to the original number of atoms in the sample given by f = N N 0 . When t = t 1 2 , we have f = 1 2 = e - λ t 1 2 Taking logarithms of both sides, ln 1 2 = - λ t 1 2 Therefore, we have λ = - ln 1 2 t 1 2 . Then the equation f = e - λ t becomes f = e ln 1 2 t t 1 2 . Thus, f = 1 2 t t 1 2 Hence, fraction f after time 2 . 5 t 1 2 is f = 1 2 t 1 2 2 . 5 t 1 2 = 0 . 177 ≈ 0 . 18

E M B I B E

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 19

EASY

AS and A Level

IMPORTANT

Earn 100

Figure shows the decay of an isotope of caesium, ${}_{55}^{134}{Cs}$ . Use the graph to determine the half-life of this nuclide in years, and hence find the decay constant in ${year}^{- 1}$ .

Important Questions on Nuclear Physics

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 20

The decay constant of a particular isotope is

3.0 \times 10^{- 4} s^{- 1}

. Calculate how long it will take for the activity of a sample of this substance to decrease to one-eighth of its initial value.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 21

The isotope ${}_{7}^{16}N$ decays with a half-life of $7.4 s$ . Calculate the decay constant for this nuclide.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 21

The isotope ${}_{7}^{16}N$ decays with a half-life of $7.4 s$ . A sample of N initially contains $5000$ nuclei. Calculate how many will remain after a time of $14.8 s$ .

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 21

The isotope ${}_{7}^{16}N$ decays with a half-life of $7.4$ . A sample of N initially contains $5000$ nuclei. Calculate how many will remain after a time of $20.0 s$ .

MEDIUM

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 22

A sample contains an isotope of half-life $t_{\frac{1}{2}}$ . Show that the fraction $f$ of nuclei in the sample that remain undecayed after a time $t$ is given by the equation:
$f = {(\frac{1}{2})}^{n}$ where $n = \frac{t}{t_{\frac{1}{2}}}$ .