The threshold frequency of sodium is 5.51 × 1014 s^−1. Calculate the kinetic energy of the electrons ejected when the surface of sodium is exposed to ultraviolet radiation of wavelength 180 nm.
Not sure if I'm correct, but I got 1.1 × 10 ^18
oops I meant 7.38 x 10^-19
To calculate the kinetic energy of the ejected electrons, we can use the equation:
Kinetic Energy = Planck's constant (h) × (frequency - threshold frequency)
First, we need to calculate the frequency of the ultraviolet radiation using the wavelength:
Speed of light (c) = wavelength × frequency
Since we know the speed of light is approximately 3.00 × 10^8 m/s, we can rearrange the equation to solve for frequency:
frequency = Speed of light / wavelength
Now, plug in the values:
frequency = (3.00 × 10^8 m/s) / (180 × 10^-9 m)
frequency ≈ 1.67 × 10^15 s^-1
Next, we can calculate the kinetic energy:
Kinetic Energy = Planck's constant (h) × (frequency - threshold frequency)
Kinetic Energy = 6.63 × 10^-34 J·s × (1.67 × 10^15 s^-1 - 5.51 × 10^14 s^-1)
Kinetic Energy ≈ 1.08 × 10^-19 J
Therefore, the kinetic energy of the electrons ejected when the surface of sodium is exposed to ultraviolet radiation of wavelength 180 nm is approximately 1.08 × 10^-19 Joules.