Answer:
The minimum energy required to remove an electron from potassium metal is 3.465 x 10⁻¹⁹ J
Explanation:
Given;
light wavelength, λ = 570nm
velocity of ejected electron, v = 6.4 x 10⁴ m/s
Minimum energy required to remove an electron from a metal surface is given as;
W₀ = hf₀
where;
W₀ is work function also known as minimum energy required
h is Planck's constant
f₀ is threshold frequency of light
Also,
E = W₀ + K.E
where;
E is the energy of the incident light
W₀ is work function
K.E is the kinetic energy of the electron
[tex]h\frac{c}{\lambda} = W_o + \frac{1}{2} mv^2\\\\W_o = h\frac{c}{\lambda} - \frac{1}{2} mv^2\\\\[/tex]
where;
m is mass of electron
c is speed of light
[tex]W_o = \frac{6.62 *10^{-34}*3*10^8}{570*10^{-9}}\ - \frac{1}{2} *9.1*10^{-31}*(6.4*10^4)^2\\\\W_o = 3.484*10^{-19} J \ - \ 0.01864*10^{-19} J\\\\W_o = 3.465 *10^{-19} J[/tex]
Therefore, the minimum energy required to remove an electron from potassium metal is 3.465 x 10⁻¹⁹ J
