1. Calculate the ratio between the wavelength of an electron and a proton if the proton is moving with half the velocity of electron.

(Mass of proton = 1.67 X 10^-27 kg, Mass of electron = 9.11 X 10^-31 kg)

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Solution

Given -
Mass of proton = 1.67 X 10^-27 kg
Mass of electron = 9.11 X 10^-31 kg
v_p = (1/2)v_e = 0.5 v_e (as given in question)
v_p = Velocity of proton
v_e₌ Velocity of electron

Wavelength of an electron (λ_e) = h/m_ev_e ........ equation 1
Wavelength of an proton (λ_p) = h/m_pv_p = h/(m_p_x 0.5 v_e)........ equation 2

Using the given values and dividing 1 by 2-

Ratio between the wavelength of an electron and a proton-
λ_e/λ_p
= (h/m_ev_e)/h/(m_p_x 0.5 v_e)
= (m_p_x 0.5 v_e)/ (m_ev_e₎
= ( 1.67 X 10^-27 x 0.5 ) /(9.11 X 10^-31 ) kg
= 916.57

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Q. Calculate the ratio between the wavelength of an electron and a proton, if the proton is moving at half the velocity of the electron (mass of the proton

= 1.67 \times 10^{- 27} k g

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1. Calculate the ratio between the wavelength of an electron and a proton if the proton is moving with half the velocity of electron. (Mass of proton = 1.67 X 10-27 kg, Mass of electron = 9.11 X 10-31 kg)

1. Calculate the ratio between the wavelength of an electron and a proton if the proton is moving with half the velocity of electron.

(Mass of proton = 1.67 X 10^-27 kg, Mass of electron = 9.11 X 10^-31 kg)