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 $= 1.67 \times 10^{- 27} k g$ ; mass of the electron $= 9.11 \times 10^{- 28} g$ ).

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Solution

Apply de Broglie equation, $λ = \frac{h}{m v}$

Wavelength of electron $= \frac{6.625 \times 10^{- 34}}{9.11 \times 10^{- 31} v}$

Wavelength of proton $= \frac{6.625 \times 10^{- 34}}{1.67 \times 10^{- 27} \times 0.5 v}$ .

Hence the ratio comes out to be $9.2455 \times 10^{- 2} m$ .

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Similar questions

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass = 9.11 × 10^–31 kg, proton mass = 1.67 × 10^–27 kg, 1 eV = 1.60 × 10^–19 J).

What is the ratio of electrostatic force and gravitational force between a proton and electron at 1 mm distance?

Mass of proton – $1.67 \times 10^{- 27} k g$

Mass of electron – $9.11 \times 10^{- 31} k g$

Charge of electron – $1.6 \times 10^{- 19} C$

What is the ratio of electrostatic force and gravitational force between a proton and electron at 1mm distance?

Mass of proton – $1.67 \times 10^{- 27}$ kg

Mass of electron – $9.11 \times 10^{- 31}$ kg

Charge of electron – $1.6 \times 10^{- 19}$ kg

Q. Calculate the wavelength (in nanometer) associated with a proton moving at

1.0 \times 10^{3} {m s}^{- 1}

.
(Mass of proton

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

and

h = 6.63 \times 10^{- 34} J s

)

Q. Calculate the mass of a proton if the charge to mass ratio of an electron is

1.758820 \times 10^{11} {C kg}^{- 1}

and it is known that the mass of a proton is 1837 times greater than the mass of an electron.

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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 =1.67×10−27kg; mass of the electron =9.11×10−28g).

Apply de Broglie equation, λ=hmvWavelength of electron =6.625×10−349.11×10−31vWavelength of proton =6.625×10−341.67×10−27×0.5v.Hence the ratio comes out to be 9.2455×10−2m.

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 $= 1.67 \times 10^{- 27} k g$ ; mass of the electron $= 9.11 \times 10^{- 28} g$ ).

Apply de Broglie equation, $λ = \frac{h}{m v}$

Wavelength of electron $= \frac{6.625 \times 10^{- 34}}{9.11 \times 10^{- 31} v}$

Wavelength of proton $= \frac{6.625 \times 10^{- 34}}{1.67 \times 10^{- 27} \times 0.5 v}$ .

Hence the ratio comes out to be $9.2455 \times 10^{- 2} m$ .