Question

​What is the wavelength of an electron that has a kinetic energy of 0.50 MeV (relativistic)?

Answer 1

The wavelength of an electron with a kinetic energy of 0.50 MeV (relativistic) is approximately 7.28 x 10^-12 m.

Step-by-step explanation:

The wavelength of an electron with a kinetic energy of 0.50 MeV can be calculated using the relativistic de Broglie equation:

λ = h/(m*c)

Where λ is the wavelength, h is Planck's constant (6.63 x 10^-34 Js), m is the mass of the electron (9.11 x 10^-31 kg), and c is the speed of light (3.00 x 10^8 m/s).

Substituting the values:

λ = (6.63 x 10^-34 Js)/((9.11 x 10^-31 kg)*(3.00 x 10^8 m/s))

λ ≈ 7.28 x 10^-12 m

Therefore, the wavelength of the electron is approximately 7.28 x 10^-12 m.

Answer 2

The wavelength of electron is
`6.99* 10^(-22)\ m`

Step-by-step explanation:

The kinetic energy of the electron is,
`E=0.5\ MeV=0.5* 10^6\ eV`

We need to find the wavelength of this electron. It can be calculated using the concept of DE-broglie wavelength as :

`\lambda=(h)/(√(2mE) )`

h is Plank's constant

m is the mass of electron

`\lambda=\frac{6.67* 10^(-34)\ J-s}{\sqrt{2* 9.1* 10^(-31)\ kg* 0.5* 10^6\ eV} }`

`\lambda=6.99* 10^(-22)\ m`

So, the wavelength of electron is
`6.99* 10^(-22)\ m`. Hence, this is the required solution.