Answer:
λ = 1.8 x 10⁻⁷ m = 180 nm
Explanation:
First we find the work function of tungsten by using the following formula:
∅ = hc/λmax
where,
∅ = work function = ?
h = Plank's Constant = 6.626 x 10⁻³⁴ J.s
c = speed of light = 3 x 10⁸ m/s
λmax = maximum wavelength for photoelectric emission = 230 nm
λmax = 2.3 x 10⁻⁷ m
Therefore,
∅ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(2.3 x 10⁻⁷ m)
∅ = 8.64 x 10⁻¹⁹ J
Now we convert Kinetic Energy of electron into Joules:
K.E = (1.5 eV)(1.6 x 10⁻¹⁹ J/1 eV)
K.E = 2.4 x 10⁻¹⁹ J
Now, we use Einstein's Photoelectric Equation:
Energy of Photon = ∅ + K.E
Therefore,
Energy of Photon = 8.64 x 10⁻¹⁹ J + 2.4 x 10⁻¹⁹ J
Energy of Photon = 11.04 x 10⁻¹⁹ J
but,
Energy of Photon = hc/λ
where,
λ = wavelength of light = ?
Therefore,
11.04 x 10⁻¹⁹ J = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/λ
λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(11.04 x 10⁻¹⁹ J)
<u>λ = 1.8 x 10⁻⁷ m = 180 nm</u>
(length of a tennis court)