Question

Hey !!

Fast moving alpha-particle are incident on a hydrogen gas sample. What minimum kinetic energy should they posses so as to ionise hydrogen atoms ?

IIT-JEE 2014

Answer 1

Hi,

Here is your answer,

Question = Fast moving alpha-particle are incident on a hydrogen gas sample. What minimum kinetic energy should they posses so as to ionise hydrogen atoms ?

Answer = To ionise, hydrogen atom must absorb a minimum of 13.6 eV energy. The required kinetic energy of α-particles will be minimum when the collision between the α-particle and hydrogen atom is completely inelastic.

The Kinetic Energy lost in collision is absorbed by the hydrogen atom. Let us consider M and m be the masses of α-particle and hydrogen atom respectively and u be the speed of α-particle before collision.

The common velocity v after collision is given by momentum conversation as

Mu = (M + m) v => v = Mu/ M + m

The loss of energy is

E = 1/2 Mu²(m/M + m) = m K/M + m

= 1/4 + 1 K = K/5

Kmin/5 = 13.6 eV

∴ Kmin = 68 eV

Hope it helps you !!

Answer 2

HERE IS YOUR ANSWER. . . . . .

Mu = (M + m) v
v = Mu /M+m

The loss of energy is

E = 1/2 Mu^2 (m/M +m)=K/
M+m

1/4 + 1K = K/5

Kmin / 5 = 13.6eV

Kmin = 68eV


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HOPE IT HELPS YOU! ! ! !