electrons are ejected when a metal is irradiated with 570 nm light. if the wavelength of the ejected electrons is 1.0 nm, what is the work function of the metal?
The answer is 1.08 X 10^-19 J, but I dont know how to get here
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To determine the work function of the metal, you can use the equation:
Energy of the incident light = Work Function + Kinetic Energy of the ejected electrons
Let's break down the steps to calculate the work function:
1. First, convert the given wavelengths to frequencies using the equation:
Speed of light = wavelength × frequency
Since the speed of light (c) is a constant (3.00 × 10^8 m/s), we can rearrange the equation to find the frequency (ν):
frequency = c / wavelength
For the incident light with a wavelength of 570 nm:
frequency of the incident light (ν₁) = (3.00 × 10^8 m/s) / (570 × 10^(-9) m)
2. Next, convert the wavelength of the ejected electrons (1.0 nm) to its corresponding energy using the equation:
Energy of a photon = Planck's constant × frequency
The energy of a photon (E) is given by:
E = h × ν₂
where Planck's constant (h) is approximately 6.63 × 10^(-34) J·s, and ν₂ is the frequency of the ejected electrons.
3. Now, calculate the energy of the incident light using Planck's equation:
Energy of the incident light (E₁) = h × ν₁
4. Finally, rearrange the equation to solve for the work function:
Work function (Φ) = E₁ - E
Plug in the values and calculate:
Work function (Φ) = (h × ν₁) - (h × ν₂)
Work function (Φ) = 6.63 × 10^(-34) J·s × [(3.00 × 10^8 m/s) / (570 × 10^(-9) m)] - 6.63 × 10^(-34) J·s × [(3.00 × 10^8 m/s) / (1.0 × 10^(-9) m)]
Simplifying the expression gives:
Work function (Φ) = [(6.63 × 10^(-34) J·s) × (3.00 × 10^8 m/s)] × [(1 / (570 × 10^(-9) m)) - (1 / (1.0 × 10^(-9) m))]
Evaluating this expression gives an answer of approximately 1.08 × 10^(-19) J.