It takes 208.4 kJ of energy to remove 1 mole of electrons from atom on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom ont eh surface of solid rubidum? What is the maximum wavelength of light capable of doing this?
If 208.4 kJ of energy will remove 6.023 x 10^23 electrons, how many kJ will we need to remove just one electrons?
Then E = hc/lambda. You know E, h is Planck's constant, c is the speed of light in m/s, and lambda is the waveldngth in meters.
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5.7
5.223e-7
5.223e-7
To find out how much energy it takes to remove a single electron from an atom on the surface of solid rubidium, we can use the given information that it takes 208.4 kJ of energy to remove 1 mole of electrons (which is equivalent to 6.023 x 10^23 electrons).
To find the energy required to remove just one electron, we need to divide 208.4 kJ by Avogadro's number (6.023 x 10^23).
Energy to remove 1 electron = 208.4 kJ / 6.023 x 10^23 ≈ 3.46 x 10^-19 kJ
So, it takes approximately 3.46 x 10^-19 kilojoules (kJ) of energy to remove a single electron from an atom on the surface of solid rubidium.
Now, to find the maximum wavelength of light capable of removing this electron, we can use the equation:
E = hc/λ
Where E is the energy required to remove an electron (3.46 x 10^-19 kJ), h is Planck's constant (6.62607004 × 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength in meters (which we need to find).
To convert the energy from kilojoules to joules, we multiply by 1000:
E = 3.46 x 10^-19 kJ * 1000 J/kJ = 3.46 x 10^-16 J
Substituting the values into the equation and solving for λ:
3.46 x 10^-16 J = (6.62607004 × 10^-34 J·s) * (2.998 x 10^8 m/s) / λ
Rearranging the equation to solve for λ:
λ = (6.62607004 × 10^-34 J·s) * (2.998 x 10^8 m/s) / (3.46 x 10^-16 J)
Calculating the value:
λ ≈ 5.749 x 10^-7 meters
Therefore, the maximum wavelength of light capable of removing a single electron from an atom on the surface of solid rubidium is approximately 5.749 x 10^-7 meters or 574.9 nm (nanometers).