Please help i don't get the answer. How much energy, in kilojoules per mole, is released when an electron makes a transition from n=5 to n=2 in an hydrogen atom?
E = 2.180E-19J x (1/4 - 1/25)
1/4 is 1/n^2 = 1/2^2 for the lower level
1/25 is 1/n^2 = 1/5^2 for the higher level
-5.10x10-19
To calculate the energy released when an electron makes a transition from n=5 to n=2 in a hydrogen atom, you can use the formula for the energy of an electron in the hydrogen atom:
E = -13.6 * (Z^2/n^2) eV
where E is the energy of the electron, Z is the atomic number (which is 1 for hydrogen), n is the principal quantum number of the electron's initial or final energy level, and eV is electron volts.
In order to convert this energy to kilojoules per mole, we need to convert from electron volts (eV) to kilojoules (kJ) and adjust for the number of moles involved.
1 eV = 1.602 × 10^(-19) kJ (conversion factor)
First, let's calculate the energy change in electron volts using the formula:
ΔE = E(final) - E(initial)
E(final) = -13.6 * (1^2/2^2) = -13.6 * (1/4) = -3.4 eV
E(initial) = -13.6 * (1^2/5^2) = -13.6 * (1/25) = -0.544 eV
ΔE = -3.4 - (-0.544) = -2.856 eV
Now, we convert the energy change to kilojoules:
ΔE (kJ) = ΔE (eV) * (1.602 × 10^(-19) kJ/1 eV)
ΔE (kJ) = -2.856 * (1.602 × 10^(-19) kJ/1 eV)
= -4.58 × 10^(-19) kJ
Lastly, we need to account for the number of moles. Since the question asks for the energy change per mole, we need to consider Avogadro's number, 6.022 × 10^23.
Energy change per mole = ΔE (kJ) * (1 mole/6.022 × 10^23 molecules)
Energy change per mole = -4.58 × 10^(-19) kJ * (1 mole/6.022 × 10^23 molecules)
= -7.60 × 10^(-43) kJ/mol
Therefore, the energy released when an electron makes a transition from n=5 to n=2 in a hydrogen atom is approximately -7.60 × 10^(-43) kJ/mol.