KVPY SX SB Exam 20141 Question Paper

Question : 37 of 120

Marks: +1, -0

The half life of a particle of mass 1.6 x 10

^{ -26}

kg is 6.9 s and a stream of such particles is travelling with the kinetic energy of a particle being 0.05 eV. The fraction of particles which will decay when they travel a distance o f 1 m is

0.1
0.01
0.001
0.0001

Validate

Solution:

KE =1/2mv^ 2

0.05 × 1.6 × 10^{–19} =1/2×1.6

× 10^{–26} × v^2

0.05 × 2 × 10^7 = v^ 2

10^6 = v ^2

v = 1000 m/sec
time taken to travel a distance of 1 m is

1/v⇒1/1000=0.001

sec
Half life of radioactive material = 6.9 sec

T_{1\/2} =0.693/λ

λ=0.693/6.9⇒0.1

fraction of particle decay in 0.001 sec or

1/1000\sec = 1 -e^{-λt}

⇒

= 1 -e^{-0.1×1/1000}

⇒

1 -e^{1/10000}

⇒ 0.0001

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