Answer to Question #107153 in Atomic and Nuclear Physics for Abdul

Question

Carbon-14 is a radioactive isotope of carbon which decays by β− emission. It has a half-life of 5700 years.
a i Explain the meaning of the term half-life.
(1 mark)
ii State the composition of a nucleus.

(2 marks)
b is produced when a nitrogen nucleus first absorbs a neutron in the atmosphere and then the resulting nuclide emits a proton.
i State the nuclear reaction equation for the production of from .

(2 marks)
ii Write down the stable nuclide into whichdecays by β− emission.

(2 marks)
c Living plants absorb carbon dioxide from the atmosphere, a small quantity of which contains. The β− activity, A0, from a living plant remains constant, but once the plant dies the activity decays according to the expression

where A is the activity at time t.
Calculate:
i the decay constant λ for

(2 marks)
ii the ratio .

Answer 1

Answer:

a) i) The half-life of a radioactive substance is a characteristic constant. It measures the time it takes for a given amount of a substance to halve due to decay and, therefore, radiation.

ii) The number of neutrons and protons in the nucleus:

Number of protons: 6

Number of neutrons: 14-6 = 8

b) i) ${^2_0}n+{^{14}_7}N\to{^{14}_6}C+{^1_1}p$

ii) ${^{14}_6}C \to{^{14}_7}N+e+v_e$

c) i) We use the equation

$λ=\frac {ln2} {t_{1/2}}$

$λ=\frac {0.693} {5730y}$

$λ=‭1,2e^{-4}‬ y^{-1}$

ii)$A={A_0}e^{-t/{t_{1/2}}}$