Answer to Question #138602 in Electric Circuits for Fletcher Madden

Question

In an experiment on the photoelectric effect using radiation of wavelength 4.00 x 10^-7m, the maximum electron energy was observed to be 1.40 x 10-19J. With radiation of wavelength 3.00 x 10^-7m the maximum energy was 3.06 x 10^-19J. Derive a value for Planck’s constant.

Answer 1

Let $K.E_{max}$ represent the maximum Kinetic energy of the electron

Let $h$ represent Planck's constant

Let $c$ represent the speed of light

Let $W_0$ represent the work fuction of the metal

Let $\lambda$ represent the wavelength of the radiation

$$h\frac{c}{ \lambda} - W_0 = K.E_{max}\\ Therefore,\\ h × \frac{3 × 10^8ms^{-1}}{4.00 × 10^{-7}m} - W_0 = 1.40 × 10^{-19}J\\ Also,\\ h × \frac{3 × 10^8ms^{-1}}{3 × 10^{-7}m} - W_0 = 3.06 × 10^{-19}J\\ 7.5 × 10^{14}s^{-1}h - W_0 = 1.40 × 10^{-19}J\hspace{1cm}(1)\\ 1 × 10^{15}s^{-1}h = 3.06 × 10^{-19}J\hspace{2cm}(2)\\ Subtracting\hspace{0.1cm}(1) from\hspace{0.1cm}(2), \\ 2.5 × 10^{14}s^{-1}h = 1.66 × 10^{-19}J\\ h = 6.64 × 10^{-34}Js$$