Question

An a- particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de-Broglie wavelengths are lambda_a and lambda_p respectively. The ratio (lambda_p)/(lambda_a), to the nearest integer, is.

Answer 1

The ratio of λa / λp to the nearest integer is  √8 ≈ 3. The ratio to the nearest integer can be calculated as follows:

• We know that Kinetic energy = K . E = q V

• Also, De Broglie wavelength = h / √(2mK.E)

                                                = h / √(2mq V)

• Ratio of wavelengths of α - particle and proton  =  λa / λp = √MaQa /√MpQp

• As it is known that alpha particle has 4 times the mass and twice the charge of a proton. Therefore,

       λa / λp =  √8 ≈ 3.