(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.
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.
1 answer
1 answer