Calculate the energy, in joules required to ionize a hydrogen atom when its electron is initially in the n=2 energy level.
E = 2.180E-18*(1/4 - 0)
To calculate the energy required to ionize a hydrogen atom when its electron is initially in the n=2 energy level, we need to determine the energy difference between the ground state (n=1) and the given energy level (n=2), and then use the equation:
E = -R_H (1/n_final^2 - 1/n_initial^2)
Where:
- E is the energy in Joules.
- R_H is the Rydberg constant for hydrogen, which is approximately 2.18 × 10^(-18) Joules.
- n_initial is the initial energy level (n=2 in this case).
- n_final is the final energy level (ionization to n=infinity).
Substituting the values into the equation, we have:
E = - (2.18 × 10^(-18) J) * (1/infinity^2 - 1/2^2)
Since we are ionizing the hydrogen atom completely, the final energy level is infinity. Therefore, 1/infinity^2 equals zero. Now we can simplify the equation:
E = - (2.18 × 10^(-18) J) * (0 - 1/4)
= - (2.18 × 10^(-18) J) * (-1/4)
= (2.18 × 10^(-18) J) * (1/4)
Performing the calculation:
E = 5.45 × 10^(-19) J
Therefore, the energy required to ionize the hydrogen atom from the n=2 energy level is approximately 5.45 × 10^(-19) Joules.