Question

What is the approximate wavelength of : a) an electron moving with energy 10 eV?

b) a photon with an elegy of 10 eV?
c) a neutron with an energy of 0.1 eV?
(Please explain)

Answer 1

(A)
`\lambda =12.375* 10^(-8)m`

(B)
`\lambda =12.375* 10^(-8)m`

(C)
`\lambda =12.375* 10^(-6)m`

Step-by-step explanation:

(a) We have given energy of the electron = 10 eV

We know that
`1eV=1.6* 10^(-19)J`

So 10 eV =
`=10* 1.6* 10^(-19)J=1.6* 10^(-18)j`

Speed of light
`c=3* 10^8m/sec`

Plank's constant
`h=6.6* 10^(-34)J-s`

Energy of electron is given by
`E=h\\u =(hc)/(\lambda )`

`1.6* 10^(-18)=(6.6* 10^(-34)* 3* 10^8)/(\lambda )`

`\lambda =12.375* 10^(-8)m`

(b) Energy of photon is also given as E =10 eV

We know that
`1eV=1.6* 10^(-19)J`

So 10 eV =
`=10* 1.6* 10^(-19)J=1.6* 10^(-18)j`

Energy of photon is given by
`E=h\\u =(hc)/(\lambda )`

Speed of light
`c=3* 10^8m/sec`

Plank's constant
`h=6.6* 10^(-34)J-s`

`1.6* 10^(-18)=(6.6* 10^(-34)* 3* 10^8)/(\lambda )`

`\lambda =12.375* 10^(-8)m`

(c) Energy of neutron is given as E= 0.1 eV

We know that
`1eV=1.6* 10^(-19)J`

So 0.1 eV =
`=10* 1.6* 10^(-19)J=1.6* 10^(-20)j`

Speed of light
`c=3* 10^8m/sec`

Plank's constant
`h=6.6* 10^(-34)J-s`

`1.6* 10^(-20)=(6.6* 10^(-34)* 3* 10^8)/(\lambda )`

`\lambda =12.375* 10^(-6)m`