The first ionization energy is the energy necessary to completely remove the outermost electron from an atom. For a Hydrogen atom this energy is 2.18 X 10^-18J. If you were to use a laser to provide this energy, what is the wavelength (in nm) of the light emitted from the laser?
To determine the wavelength of the light emitted from the laser, we can use the equation that relates energy and wavelength:
E = hc/λ
Where:
E = energy (in joules)
h = Planck's constant (6.62607015 × 10^-34 J·s)
c = speed of light (2.998 × 10^8 m/s)
λ = wavelength (in meters)
First, we need to convert the ionization energy from joules to electron volts (eV):
1 eV = 1.60218 × 10^-19 J
Ionization energy (E) = 2.18 × 10^-18 J
Converting to eV:
E = (2.18 × 10^-18 J) / (1.60218 × 10^-19 J/eV)
E ≈ 13.605 eV
Next, solve for wavelength (λ) in meters:
λ = hc/E
λ = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (13.605 eV * 1.60218 × 10^-19 J/eV)
λ ≈ 9.102 × 10^-8 meters
To convert to nanometers, multiply by 10^9:
λ ≈ 9.102 × 10^-8 meters * 10^9 nm/meter
Therefore, the wavelength of the light emitted from the laser is approximately 91.02 nm.
To find the wavelength of the light emitted from the laser, we can use the relationship between energy and wavelength given by the equation
E = hc/λ,
where E represents the energy, h is Planck's 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 this case, we know the energy (E) required is given as 2.18 x 10^-18 J. We can rearrange the equation to solve for the wavelength (λ):
λ = hc/E.
Plugging in the given values, we have:
λ = (6.626 x 10^-34 J s * 3.00 x 10^8 m/s) / (2.18 x 10^-18 J).
Simplifying the equation gives:
λ = 9.10 x 10^-7 m.
Finally, to convert the wavelength to nanometers (nm), we multiply by 10^9:
λ = 9.10 x 10^-7 m * 10^9 nm/m,
which gives the wavelength as:
λ = 910 nm.
Therefore, the wavelength of the light emitted from the laser is 910 nm.