Question

Potassium and gold cathodes are used in a photoelectric-effect experiment. For each cathode, find: The threshold frequency. The threshold wavelength. The maximum electron ejection speed if the light has a wavelength of 210 nm . The stopping potential if the wavelength is 210 nm . Throughout this problem, be sure to use 6.63×10−34J⋅s for Planck's constant.A) The threshold frequency of potassium in hertz.B) The threshold frequency of gold in hertzC) The threshold wavelength of potassium in nanometers.D) The threshold wavelength of gold in nanometers.

Answer 1

The threshold frequency for potassium is 4.83×1014 Hz with a corresponding threshold wavelength of 621 nm. For gold, the threshold frequency is 1.16×1015 Hz with a threshold wavelength of 258 nm.

Step-by-step explanation:

To find the threshold frequency and wavelength for potassium and gold, we use the work function information provided and Planck's constant. The work function represents the minimum energy required to eject an electron from the metal surface, which corresponds to the threshold frequency (fthreshold) and the threshold wavelength (λthreshold). For converting energy from electron volts (eV) to joules (J), we use the conversion factor 1 eV = 1.602×10−16 J.

For Potassium:

The work function is 2.0 eV, which equals 3.204×10−19 J. The threshold frequency can be calculated using the formula:

fthreshold = Work Function / Planck's constant

fthreshold = 3.204×10−19 J / 6.63×10−34 J·s = 4.83×1014 Hz

The threshold wavelength is found using λ = c/f, where c is the speed of light (c = 3×108 m/s).

λthreshold = 3×108 m/s / 4.83×1014 Hz = 621 nm

For Gold:

The work function is 4.82 eV, which equals 7.72×10−19 J. Using similar calculations:

fthreshold = 7.72×10−19 J / 6.63×10−34 J·s = 1.16×1015 Hz

λthreshold = 3×108 m/s / 1.16×1015 Hz = 258 nm

Answer 2

In the photoelectric effect experiment, the threshold frequency and threshold wavelength can be determined for each cathode (potassium and gold). The threshold frequency is the minimum frequency of light required to eject an electron from a metal surface. The threshold wavelength can be calculated using the equation: threshold wavelength = speed of light / threshold frequency. The maximum electron ejection speed and stopping potential can also be calculated using specific equations.

Step-by-step explanation:

In the photoelectric effect experiment, the threshold frequency and threshold wavelength can be determined for each cathode (potassium and gold). The threshold frequency is the minimum frequency of light required to eject an electron from a metal surface. It can be calculated using the equation:

threshold frequency = work function / Planck's constant

Similarly, the threshold wavelength can be calculated using the equation:threshold wavelength = speed of light / threshold frequency

The maximum electron ejection speed and stopping potential can be calculated using the equation:maximum electron ejection speed = (wavelength of light / threshold wavelength) * speed of light stopping potential = (Plank's constant * threshold frequency) / electron charge

For potassium, the work function is given as 2.0 eV. Using the equation:

threshold frequency = (2.0 eV * 1.6 x 10⁻¹⁹ J/eV) / (6.63 x 10⁻³⁴ J.s)

For gold, the work function is not provided. Therefore, it cannot be determined without additional information.

Let's calculate the threshold frequency and threshold wavelength for potassium:

threshold frequency = (2.0 eV * 1.6 x 10⁻¹⁹ J/eV) / (6.63 x 10⁻³⁴ J.s)

threshold wavelength = (3 x 10⁸ m/s) / threshold frequency