Question

The ratio of de Broglie wavelengths of a deuterium atom to that of an α - particle, when the velocity of the former is five times greater than that of later, is

Answer 1

Conditions for Deuterium ⇒

Let the Velocity of the Deuterium be v m/s.

Mass = 2 u

∴ Wavelength of Deuterium = h/2v [ By De-Broglie Principles]

Conditions for the alpha - particle,

Mass = 4 u

Velocity of alpha particle = v/5

∴ Wavelength of alpha particle = (h/4)/(v/5) [ By De-Broglie Principles]

= 5h/4v

Now,

Ratio of wavelength of Deuterium to alpha particle = (h/2v)/(5h/4v )

= 4/10

= 2/5

Hence the Ratio is 2 : 5.

Hope it helps.

Answer 2

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