# Potassium-40 Can Decay in Three Modes. It Can Decay by β−-emission, B*-emission of Electron Capture. (A) Write the Equations Showing the End Products. (B) Find the Q-values - Physics

Sum

Potassium-40 can decay in three modes. It can decay by β-emission, B*-emission of electron capture. (a) Write the equations showing the end products. (b) Find the Q-values in each of the three cases. Atomic masses of ""_18^40Ar , ""_19^40K and ""_20^40Ca are 39.9624 u, 39.9640 u and 39.9626 u respectively.

(Use Mass of proton mp = 1.007276 u, Mass of ""_1^1"H" atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

#### Solution

(a) Decay of potassium-40 by βemission is given by

""_19"K"^40 → ""_20"Ca"^40 + β^- + bar"v"

Decay of potassium-40 by β+ emission is given by

""_19"K"^40 → ""_18"Ar"^40 + β^+ + "v"

Decay of potassium-40 by electron capture is given by

""_19"K"^40 + e^(-) → ""_18"Ar"^40 + "v"

(b)

Qvalue in the β decay is given by
Qvalue = [m(19K40) − m(20Ca40)]c2
= [39.9640 u − 39.9626 u]c2
= 0.0014  xx 931 MeV
= 1.3034 MeV

Qvalue in the β+ decay is given by
Qvalue = [m(19K40) − m(20Ar40) − 2me]c2
= [39.9640 u − 39.9624 u −  0.0021944 u]c2
= (39.9640 − 39.9624) 931 MeV − 1022 keV
= 1489.96 keV − 1022 keV
= 0.4679 MeV

Qvalue in the electron capture is given by
Qvalue = [ m(19K40) − m(20Ar40)]c2
= (39.9640 − 39.9624)uc2
= 1.4890 = 1.49 MeV

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 24 The Nucleus
Q 14 | Page 442