Question

By what potential difference must a proton [m_0 = 1.67E-27 kg) be accelerated to have a wavelength lambda = 4.23E-12 m? By what potential difference must an electron [m_0 = 9.11E-31 kg), be accelerated to have a wavelength lambda = 4.23E-12 m?

Answer 1

Step-by-step explanation:

1. Mass of the proton,
`m_p=1.67* 10^(-27)\ kg`

Wavelength,
`\lambda_p=4.23* 10^(-12)\ m`

We need to find the potential difference. The relationship between potential difference and wavelength is given by :

`\lambda=(h)/(√(2m_pq_pV))`

`V=(h^2)/(2q_pm_p\lambda^2)`

`V=((6.62* 10^(-34))^2)/(2* 1.6* 10^(-19)* 1.67* 10^(-27)* (4.23* 10^(-12))^2)`

V = 45.83 volts

2. Mass of the electron,
`m_p=9.1* 10^(-31)\ kg`

Wavelength,
`\lambda_p=4.23* 10^(-12)\ m`

We need to find the potential difference. The relationship between potential difference and wavelength is given by :

`\lambda=(h)/(√(2m_eq_eV))`

`V=(h^2)/(2q_em_e\lambda^2)`

`V=((6.62* 10^(-34))^2)/(2* 1.6* 10^(-19)* 9.1* 10^(-31)* (4.23* 10^(-12))^2)`

`V=6.92* 10^(34)\ V`

V = 84109.27 volt

Hence, this is the required solution.