Question

What is the De Broglie wavelength of

(a) 1 eV electron

(b) 10 MeV proton

(c) 100 MeV electron? (You might need to use the relativistic energy formula for ©

Answer 1

(a). The wave length of 1 eV electron is
`1.23*10^(-9)\ m`.

(b). The wave length of 10 MeV proton is
`9.06*10^(-15)\ m`.

(c). The wave length of 100 MeV electron is
`1.23*10^(-13)\ m`.

Step-by-step explanation:

Given that,

`E =1\ ev`

`E=10 MeV`

`E=100 MeV`

(a). We need to calculate the wavelength of 1 eV electron

Using formula of De Broglie wavelength

`\lambda=(h)/(√(2mE))`

`\lambda=\frac{6.63*10^(-34)}{\sqrt{2*9.1*10^(-31)*1*1.6*10^(-19)}}`

`\lambda=1.23*10^(-9)\ m`

`\lambda=1.23\ nm`

The wave length of 1 eV electron is
`1.23*10^(-9)\ m`.

(b). We need to calculate the wavelength of 10 MeV proton

Using formula of De Broglie wavelength

`\lambda=(h)/(√(2mE))`

Put the value into the formula

`\lambda=\frac{6.63*10^(-34)}{\sqrt{2*1.67*10^(-27)*10*10^(6)*1.6*10^(-19)}}`

`\lambda=\frac{6.63*10^(-34)}{\sqrt{5.344*10^(-39)}}`

`\lambda=9.06*10^(-15)\ m`

The wave length of 10 MeV proton is
`9.06*10^(-15)\ m`.

(c). We need to calculate the wavelength of 100 MeV electron

Using formula of De Broglie wavelength

`\lambda=(h)/(√(2mE))`

Put the value into the formula

`\lambda=\frac{6.63*10^(-34)}{\sqrt{2*9.1*10^(-31)*100*10^(6)*1.6*10^(-19)}}`

`\lambda=1.23*10^(-13)\ m`

The wave length of 100 MeV electron is
`1.23*10^(-13)\ m`.

Hence, This is the required solution.