what is the binding energy of an electron in a photosensitive metal (in kj/mol) if the minimum frequency of light that can eject electrons from the metal is 6.3 x 20^14 Hz?
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To find the binding energy of an electron in a photosensitive metal, we need to use the equation that relates the energy of a photon to its frequency.
The energy of a photon (E) can be calculated using the equation:
E = h * f
where:
E is the energy of the photon,
h is Planck's constant (6.626 x 10^-34 J·s),
f is the frequency of the light.
Since the given frequency is 6.3 x 10^14 Hz, we can substitute this value into the equation:
E = (6.626 x 10^-34 J·s) * (6.3 x 10^14 Hz)
To convert the energy from joules (J) to kilojoules (kJ) and the frequency from Hz to s^-1, we can use the following conversion factors:
1 J = 10^-3 kJ
1 Hz = 1 s^-1
Therefore, the binding energy can be calculated as follows:
E = (6.626 x 10^-34 J·s) * (6.3 x 10^14 Hz) * (1 J / 1 s^-1) * (1 kJ / 10^3 J)
Calculating this expression, we find:
E = 6.626 x 6.3 x 10^-34 x 10^14 x 10^-3 kJ
Simplifying the expression, we get:
E ≈ 41.61 kJ/mol
Therefore, the binding energy of an electron in a photosensitive metal, given that the minimum frequency of light that can eject electrons is 6.3 x 10^14 Hz, is approximately 41.61 kJ/mol.
To calculate the binding energy of an electron in a photosensitive metal, we can use the equation:
E = hf
where E is the energy, h is the Planck constant (6.62607015 x 10^-34 J·s), and f is the frequency of light.
First, we need to convert the given frequency from Hz to s^-1:
Frequency = 6.3 x 10^14 Hz
Now, we will calculate the energy:
E = (6.62607015 x 10^-34 J·s) * (6.3 x 10^14 s^-1)
E ≈ 4.16 x 10^-19 J
To convert from joules to kilojoules, we divide the energy by 1000:
Binding Energy ≈ (4.16 x 10^-19 J) / 1000 ≈ 4.16 x 10^-22 kJ/mol
Therefore, the binding energy of an electron in a photosensitive metal is approximately 4.16 x 10^-22 kJ/mol.