(a). The wave length of 1 eV electron is
.
(b). The wave length of 10 MeV proton is
.
(c). The wave length of 100 MeV electron is
.
Explanation:
Given that,
![E =1\ ev](/tpl/images/0272/0964/4b671.png)
![E=10 MeV](/tpl/images/0272/0964/984be.png)
![E=100 MeV](/tpl/images/0272/0964/2d0ea.png)
(a). We need to calculate the wavelength of 1 eV electron
Using formula of De Broglie wavelength
![\lambda=\dfrac{h}{\sqrt{2mE}}](/tpl/images/0272/0964/81c37.png)
![\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times9.1\times10^{-31}\times1\times1.6\times10^{-19}}}](/tpl/images/0272/0964/38eca.png)
![\lambda=1.23\times10^{-9}\ m](/tpl/images/0272/0964/cdc71.png)
![\lambda=1.23\ nm](/tpl/images/0272/0964/5361f.png)
The wave length of 1 eV electron is
.
(b). We need to calculate the wavelength of 10 MeV proton
Using formula of De Broglie wavelength
![\lambda=\dfrac{h}{\sqrt{2mE}}](/tpl/images/0272/0964/81c37.png)
Put the value into the formula
![\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times1.67\times10^{-27}\times10\times10^{6}\times1.6\times10^{-19}}}](/tpl/images/0272/0964/4b788.png)
![\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{5.344\times10^{-39}}}](/tpl/images/0272/0964/8c91e.png)
![\lambda=9.06\times10^{-15}\ m](/tpl/images/0272/0964/d5ba7.png)
The wave length of 10 MeV proton is
.
(c). We need to calculate the wavelength of 100 MeV electron
Using formula of De Broglie wavelength
![\lambda=\dfrac{h}{\sqrt{2mE}}](/tpl/images/0272/0964/81c37.png)
Put the value into the formula
![\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times9.1\times10^{-31}\times100\times10^{6}\times1.6\times10^{-19}}}](/tpl/images/0272/0964/e446d.png)
![\lambda=1.23\times10^{-13}\ m](/tpl/images/0272/0964/572ca.png)
The wave length of 100 MeV electron is
.
Hence, This is the required solution.