Question

An energy of 6.8 x 10^-19 J/atom is required to cause an aluminum atom on a metal surface to lose an electron.

Calculate the longest possible wavelength of light that can ionize an aluminum atom.

Wavelength = ?m

Answer 1

Wavelength of the light is 2.9 × 10⁻⁷ m.

Step-by-step explanation:

Planck - Einstein equation shows the relationship between the energy of a photon and its frequency, and they are directly proportional to each other and it is given by the equation as E = hν,

where E is the energy of the photon

h is the Planck's constant = 6.626 × 10⁻³⁴ J s

ν is the frequency

From the above equation, we can find the frequency by rearranging the equation as,

ν =
`$ (E)/(h)` =
`$ (6.8 * 10^(-19))/(6.626*10^(-34)) = 1.03*10^(15) s^(-1)`

Now the frequency and the wavelength are in inverse relationship with each other.

ν × λ = c

It can be rearranged to get λ as,

λ = c / ν

=
`$(3* 10^(8) ms^(-1))/(1.03*10^(15)s^(-1)) = 2.9* 10^(-7) m`

So wavelength is 2.9 × 10⁻⁷ m.