Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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197 80 Hg Decay to 197 79 Au Through Electron Capture with a Decay Constant of 0.257 per Day. (A) What Other Particle Or Particles Are Emitted in the Decay? - Physics

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Question

`""_80^197`Hg decay to `""_79^197`Au through electron capture with a decay constant of 0.257 per day. (a) What other particle or particles are emitted in the decay? (b) Assume that the electron is captured from the K shell. Use Moseley's law √v = a(Z − b) with a = 4.95 × 107s−1/2 and b = 1 to find the wavelength of the Kα X-ray emitted following the electron capture.

Solution

Given:
Decay constant of electron capture = 0.257 per day
(a) The reaction is given as

`""_80^197`Hg + e → `""_79^197`Au + `"v"`

The other particle emitted in this reaction is neutrino v.

(b) Moseley's law is given by

`sqrtv = a(Z - b)`

We  know
`v = c/lambda`
Here, c = Speed of light
         `lambda` = Wavelength of the Kα X-ray

`sqrt(c/lambda) = 4.95 xx 10^7(79 - 1)`

= `4.95 xx 10^7 xx 78`

⇒ `c/lambda = (4.95 xx 78)^2 xx 10^14`

⇒`lambda = (3 xx 10^8)/(149073.21 xx 10^14)`

 = 20 `"pm"`

  Is there an error in this question or solution?

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Solution 197 80 Hg Decay to 197 79 Au Through Electron Capture with a Decay Constant of 0.257 per Day. (A) What Other Particle Or Particles Are Emitted in the Decay? Concept: Radioactivity - Introduction of Radioactivity.
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