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.

Answer 1

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

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 = $\frac{E}{h}$ = $\frac{6.8 \times 10^{-19}}{6.626\times10^{-34}} = 1.03\times10^{15} s^{-1}$

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

 = $\frac{3\times 10^{8} ms^{-1}}{1.03\times10^{15}s^{-1}} = 2.9\times 10^{-7} m$

So wavelength is 2.9 × 10⁻⁷ m.