Question

What are the de Broglie frequencies and wavelengths of (a) an electron accelerated to 50 eV and (2 pts) (b) a proton accelerated to 50 eV? (2 pts)

Answer 1

what

Step-by-step explanation:

Answer 2

Step-by-step explanation:

(a) An electron accelerated from rest through a potential difference of 100 V. The De Broglie wavelength in terms of potential difference is given by :

`\lambda=(h)/(√(2meV) )`

Where

m and e are the mass of and charge on an electron

Here, eV = 50 eV

`\lambda=\frac{6.67* 10^(-34)}{\sqrt{2* 9.1* 10^(-31)* 50} }`

`\lambda=6.99* 10^(-20)\ m`

The frequency of electron is given by :

`f=(c)/(\lambda)`

`f=(3* 10^8)/(6.99* 10^(-20))`

`f=4.29* 10^(27)\ Hz`

(b) The mass of the proton,
`m=1.67* 10^(-27)\ kg`

The De Broglie wavelength is given by :

`\lambda=\frac{6.67* 10^(-34)}{\sqrt{2* 1.67* 10^(-27)* 50}}`

`\lambda=1.63* 10^(-21)\ m`

The frequency of proton is given by :

`f=(c)/(\lambda)`

`f=(3* 10^8)/(1.63* 10^(-21))`

`f=1.84* 10^(29)\ Hz`

Hence, this is the required solution.