It takes 208.4 kJ of energy to remove 1 mole of electrons from 1 mole of atoms on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium in Joules?
What is the maximum wavelength of light capable of doing this in nanometers?
208,400/6.022E23 = Energy/atom.
Eatom = hc/wavelength. Solve for wavelength, in meters, and convert to nm.
To find out the energy required to remove a single electron from an atom on the surface of solid rubidium in Joules, we can convert the given energy value from kilojoules to joules and then divide it by Avogadro's number (6.022 x 10^23) to account for 1 mole of atoms. Here's how you do it:
1. Convert the energy from kilojoules to joules:
208.4 kJ x 1000 = 208,400 J
2. Divide the energy by Avogadro's number:
208,400 J / 6.022 x 10^23 = 3.458 x 10^-19 J (rounded to 3 decimal places)
Therefore, it takes approximately 3.458 x 10^-19 Joules of energy to remove a single electron from an atom on the surface of solid rubidium.
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, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength. We can rearrange this equation to solve for λ. Here's how:
1. Substitute the known values into the equation:
3.458 x 10^-19 J = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s) / λ
2. Rearrange the equation to solve for λ:
λ = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s) / 3.458 x 10^-19 J
3. Calculate the wavelength:
λ = 5.716 x 10^-7 meters (rounded to 3 decimal places)
Since the wavelength is in meters, to convert it to nanometers, you can multiply the value by 10^9:
λ (in nm) = 5.716 x 10^-7 meters x 10^9 nm/m = 571.6 nm (rounded to the nearest whole number)
Therefore, the maximum wavelength of light capable of removing an electron from an atom on the surface of solid rubidium is approximately 571.6 nanometers.