calculate the:
(a) energy required to excite the hydrogen electron from its ground state to level n=2, and
(b) wavelength of light that must be absorbed by an hydrogen atom in its ground state to reach the excited state.
(a) The energy required to excite an electron in a hydrogen atom from the ground state to level n=2 can be calculated using the formula:
E = -13.6 eV * (1/n^2)
Where E is the energy in electron volts (eV) and n is the principal quantum number of the excited state. Plugging in n=2:
E = -13.6 eV * (1/2^2)
E = -13.6 eV * (1/4)
E = -13.6/4 eV
E = -3.4 eV
Therefore, the energy required to excite the hydrogen electron from its ground state to level n=2 is 3.4 eV.
(b) The wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach the excited state can be calculated using the formula:
E = hc/λ
Where E is the energy in joules, h is the Planck 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 in meters. Converting the energy required to joules:
E = 3.4 eV * 1.602 x 10^-19 J/eV
E = 5.45 x 10^-19 J
Now, plug in the values into the formula:
5.45 x 10^-19 J = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/λ
λ = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/(5.45 x 10^-19 J)
λ = 3.64 x 10^-7 m
Therefore, the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach the excited state is 364 nm.