Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state of n=4 if it requires an energy of at least 1.36 x10^-19 J to do this.
Please help with formulas to use?
1/wavelength = R[1/(N^2)1 -1/(N^2)]2
R = 1.07937E7 in meters
N1 = 4 so N^ is 16
N2 is infinity so 1/infinity = 0
To calculate the maximum wavelength of light capable of removing an electron from the energy state of n=4 for a hydrogen atom, we can use the energy equation for a photon:
E = hc/λ
Where:
- E is the energy of the photon
- h is the Planck's constant (6.62607015 × 10^-34 J·s)
- c is the speed of light in a vacuum (2.998 × 10^8 m/s)
- λ is the wavelength of the light
Since we know that it requires at least 1.36 x 10^-19 J of energy to remove the electron, we can substitute these values into the equation to solve for the maximum wavelength:
1.36 x 10^-19 J = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) / λ
Now, let's rearrange the equation to solve for λ:
λ = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) / 1.36 x 10^-19 J
Performing the calculations:
λ = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (1.36 x 10^-19 J)
λ = 1.46 × 10^-7 m
Therefore, the maximum wavelength of light capable of removing an electron from the energy state of n=4 for a hydrogen atom is approximately 1.46 × 10^-7 meters (or 146 nm).