the longest wavelength of light that will cause an electron to be emitted from a metal is 520nm. what is the work function for this metal? (note: the work function is given as kJ/mole of electrons released)
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To find the work function of the metal, we can use the equation:
Energy of a photon = Work function + Kinetic energy of the emitted electron
The energy of a photon is given by the equation:
Energy of a photon = (Planck's constant) × (speed of light) / (wavelength)
First, let's convert the given wavelength from nanometers (nm) to meters (m):
520 nm = 520 × 10^(-9) m = 5.2 × 10^(-7) m
Now, we can find the energy of a photon:
Energy of a photon = (6.626 × 10^(-34) J·s) × (3.00 × 10^8 m/s) / (5.2 × 10^(-7) m)
= 3.80 × 10^(-19) J
Since the work function is given as kilojoules (kJ) per mole of electrons released, we need to convert the energy of a photon from joules (J) to kilojoules (kJ):
3.80 × 10^(-19) J = (3.80 × 10^(-19) J) × (1 kJ / 1000 J)
≈ 3.80 × 10^(-22) kJ
Therefore, the work function for this metal is approximately 3.80 × 10^(-22) kJ/mole of electrons released.