Question

(a) what wavelength photon would you need to ionize a hydrogen atom (ionization energy = 13.6 eV)? (b) Compute the temperature of the blackbody whose spectrum peaks at wavelength you found in (a).

Answer 1

(a). The wavelength of photon is 914 A.

(b). The temperature of the black body whose spectrum peaks at wavelength is 31706.78 K.

Step-by-step explanation:

Given that,

Ionization energy = 13.6 eV

(a). We need to calculate the wavelength

Using formula of wavelength

`E=(hc)/(\lambda)`

`\lambda=(hc)/(E)`

Where, h = Planck constant

c = speed of light

E = energy

Put the value into the formula

`\lambda=(6.63*10^(-34)*3*10^(8))/(13.6*1.6*10^(-19))`

`\lambda=9.14*10^(-8)\ m`

`\lambda=914\ \AA`

The wavelength of photon is 914 A.

(b). We need to calculate the temperature of the black body whose spectrum peaks at wavelength

Using Wien's displacement law

`\lambda_(max) T=2.898*10^(-3)`

`T=(2.898*10^(-3))/(\lambda)`

Put the value of wavelength

`T=(2.898*10^(-3))/(914*10^(-10))`

`T=31706.78\ K`

The temperature of the black body whose spectrum peaks at wavelength is 31706.78 K.

Hence, This is the required solution.