Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts?

Question

Answer

Calculation of Wavelength of an Electron Accelerated through Potential Difference of 100 Million Volts

Explanation

When an electron is accelerated through a potential difference, it gains kinetic energy, which can be calculated using the formula:

Kinetic Energy (K) = qV

where q is the charge of the electron and V is the potential difference.

The de Broglie wavelength of the electron can be calculated using the formula:

λ = h/p

where λ is the wavelength, h is Planck's constant, and p is the momentum of the electron.

The momentum of the electron can be calculated using the formula:

p = sqrt(2mK)

where m is the mass of the electron.

Calculation

Given that the potential difference is 100 million volts, the kinetic energy gained by the electron can be calculated as:

K = (1.6 x 10^-19 C) x (100 x 10^6 V) = 1.6 x 10^-12 J

The momentum of the electron can be calculated as:

p = sqrt(2 x (9.11 x 10^-31 kg) x (1.6 x 10^-12 J)) = 1.825 x 10^-21 kg m/s

Finally, the de Broglie wavelength of the electron can be calculated as:

λ = (6.626 x 10^-34 J s) / (1.825 x 10^-21 kg m/s) = 3.63 x 10^-13 m

Therefore, the wavelength of the electron accelerated through a potential difference of 100 million volts is 3.63 x 10^-13 meters.

Answer

Energy =qv
where q= charge on electron
v= potential difference
now wavelength = h/√2mqv
calculate the wavelength
m is mass of electron

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