Find the de Broglie wavelength of an electron

[Reshma]

Find the de Broglie wavelength of an electron with KE:
a]10eV
b]1KeV
c]1MeV
d]100MeV

Formulae:
Relativistic
$$\lambda = \frac{h}{\sqrt{{(E/c)}^2 - m_0^2c^4}}$$

Non-relativistic
$$\lambda = \frac{h}{\sqrt{2mE}}$$

I am wondering for which case(s) should I apply the relativistic or the non-relativistic equation given that the BE of electron is 0.511MeV.

 

[inha]

The nonrelativistic approximation is generally good enough until the KE is about 5 or 10% of the rest energy.

 

[Andrew Mason]

Find the de Broglie wavelength of an electron with KE:
a]10eV
b]1KeV
c]1MeV
d]100MeV

Formulae:
Relativistic
$$\lambda = \frac{h}{\sqrt{{(E/c)}^2 - m_0^2c^4}}$$

Non-relativistic
$$\lambda = \frac{h}{\sqrt{2mE}}$$

I am wondering for which case(s) should I apply the relativistic or the non-relativistic equation given that the BE of electron is 0.511MeV.

If the energy of the electron is much less than this, the electron is non-relativistic. Otherwise use the relativistic formula.

AM

 

[Reshma]

Thanks inha and Andrew for the help!