The isotope nitrogen- 13 has a half-life of 10 min . A sample initially contains 8 . 0 × 10 10 undecayed nuclei. Write down an equation to show how the number undecayed N depends on time t .

The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay. The nuclide which undergoes decay in a radioactive process is a parent nuclide, and the nuclide which is produced in the radioactive process is a daughter nuclide. Radioactive decay equation is given by N = N 0 e - λ t where, N 0 is the initial amount of nuclei and λ is decay constant.

The isotope nitrogen- 13 has a half-life of 10 min . A sample initially contains 8 . 0 × 10 10 undecayed nuclei. Write down an equation to show how the number undecayed N depends on time t .

The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay. The nuclide which undergoes decay in a radioactive process is a parent nuclide, and the nuclide which is produced in the radioactive process is a daughter nuclide. Radioactive decay equation is given by N = N 0 e - λ t where, N 0 is the initial amount of nuclei and λ is decay constant.

The isotope nitrogen-13 has a half-life of 10 min . A sample initially contains 8 . 0 × 10 10 undecayed nuclei. Calculate how many undecayed nuclei will remain after 10 min , and after 20 min .

Given half life of isotope nitrogen- 13 is 10 min . We know that half life is the time a radioactive substance takes for a given amount of the substance to become reduced by half as a consequence of decay, and therefore, with the emission of radiation. So, after 10 minutes, half the nuclei will decay, so half will remain undecayed, or 4 . 0 × 10 10 . After a further 10 minutes, half the remaining number will decay, leaving one-quarter of the original number, or 2 . 0 × 10 10 undecayed nuclei.

The isotope nitrogen-13 has a half-life of 10 min . A sample initially contains 8 . 0 × 10 10 undecayed nuclei. Determine how many nuclei will decay during the first 30 min .

Given half life of isotope nitrogen- 13 is 10 min . We know that half life is the time a radioactive substance takes for a given amount of the substance to become reduced by half as a consequence of decay, and therefore, with the emission of radiation. So, after 30 min , three half lives have elapsed. Number of original nuclei decaying in this time = 1 2 + 1 4 + 1 8 = 7 8 of the total initial amount. The number of nuclei that decay during the first 30 min = 7 8 × 8 × 10 10 = 7 × 10 10

A sample of an isotope for which λ = 0 . 10 s - 1 contains 5 . 0 × 10 9 undecayed nuclei at the start of an experiment. Determine its activity after 50 s .

Using radioactive decay equation, number of nuclei left after time t is N = N 0 e - λ t where, N 0 is undecayed nuclei at the start. Putting the values, we get N = 5 × 10 9 × e - 0 . 1 × 50 = 3 . 37 × 10 7 ≈ 3 . 4 × 10 7 Now, the activity A = λ N = 0 . 1 × 3 . 4 × 10 7 = 3 . 4 × 10 6 Bq

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The isotope nitrogen- $13$ has a half-life of $10 \min$ . A sample initially contains $8.0 \times 10^{10}$ undecayed nuclei. Write down an equation to show how the number undecayed $N$ depends on time $t$ .

Important Questions on Nuclear Physics

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Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 16

The isotope nitrogen-13 has a half-life of $10 \min$ . A sample initially contains $8.0 \times 10^{10}$ undecayed nuclei. Calculate how many undecayed nuclei will remain after $10 \min$ , and after $20 \min$ .

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Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 16

The isotope nitrogen-13 has a half-life of $10 \min$ . A sample initially contains $8.0 \times 10^{10}$ undecayed nuclei. Determine how many nuclei will decay during the first $30 \min$ .

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Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 17

A sample of an isotope for which $λ = 0.10 s^{- 1}$ contains $5.0 \times 10^{9}$ undecayed nuclei at the start of an experiment. Determine the number of undecayed nuclei after $50 s$ .

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Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 17

A sample of an isotope for which $λ = 0.10 s^{- 1}$ contains $5.0 \times 10^{9}$ undecayed nuclei at the start of an experiment. Determine its activity after $50 s$ .

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Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>Questions>Q 18

The value of $λ$ for protactinium- $234$ is $9.6 \times 10^{- 3} s^{- 1} .$ Table, shows the number of undecayed nuclei $N$ in a sample. Copy and complete Table. Draw a graph of N against t, and use it to find the half-life $t_{\frac{1}{2}}$ of protactinium- $234$ .

t / s	0	20	40	60	80	100	120	140
N	400	330

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

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 ${year}^{- 1}$ .

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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.

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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.

The isotope nitrogen-13 has a half-life of 10 min. A sample initially contains 8.0×1010 undecayed nuclei. Write down an equation to show how the number undecayed N depends on time t.

Important Questions on Nuclear Physics

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The isotope nitrogen- $13$ has a half-life of $10 \min$ . A sample initially contains $8.0 \times 10^{10}$ undecayed nuclei. Write down an equation to show how the number undecayed $N$ depends on time $t$ .