Calculate the wavelength of light that must be absorbed by hydrogen atom in its ground state to reach the excited ste of E=+2.914*10^(-18)
E = hc/λ where h = 6.626 E -34 Js
+2.914*10^(-18) J = [6.626*10^(-34) Js (3*10^8) m/s] / λ
so do some mathematical manipulation and isolate λ to get:
λ = [6.626*10^(-34) Js (3*10^8) m/s] / +2.914*10^(-18) J
& you can use a calculator to get the final answer :)
Well, let me grab my trusty calculator here... *squeaks* So, the energy difference between the ground state and the excited state of hydrogen is E = 2.914 * 10^(-18) joules.
To calculate the wavelength, we can use the equation E = hc/λ, where h is Planck's constant (6.626 x 10^(-34) J*s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength.
Rearranging the equation to solve for λ, we have λ = hc/E.
Substituting in the values, we get λ = (6.626 x 10^(-34) J*s * 3.0 x 10^8 m/s) / (2.914 x 10^(-18) J).
And after crunching the numbers (drum roll, please)... *cymbals clash* we find that the wavelength of light required to go from the ground state to the excited state is approximately 2.152 x 10^(-7) meters.
But hey, don't worry, I won't leave you hanging without a joke. Why did the scarecrow win an award? Because it was outstanding in its field!
To calculate the wavelength of light that must be absorbed by a hydrogen atom, we can use the equation:
ΔE = E2 - E1 = hc / λ
Where:
ΔE = change in energy (E2 - E1)
E2 = energy of the excited state
E1 = energy of the ground state
h = Planck's constant (6.626 x 10^(-34) J·s)
c = speed of light (3 x 10^8 m/s)
λ = wavelength of light
Given:
E2 = +2.914 x 10^(-18) J
In the ground state, the energy of a hydrogen atom is E1 = -13.6 eV. To convert to Joules, we multiply by the electron volt-to-Joule conversion factor of 1.602 x 10^(-19) J/eV:
E1 = -13.6 eV × (1.602 x 10^(-19) J/eV) = -2.182 x 10^(-18) J
Now we can substitute these values into the equation and solve for λ:
ΔE = E2 - E1
ΔE = +2.914 x 10^(-18) J - (-2.182 x 10^(-18) J)
ΔE = +5.096 x 10^(-18) J
Now rearrange the equation to solve for λ:
λ = hc / ΔE
Substituting the values of h, c, and ΔE:
λ = (6.626 x 10^(-34) J·s × 3 x 10^8 m/s) / (5.096 x 10^(-18) J)
λ = (19.878 x 10^(-26) J·m) / (5.096 x 10^(-18) J)
Divide the numerator by the denominator:
λ = 3.8995 x 10^(-8) m
Therefore, the wavelength of light that must be absorbed by the hydrogen atom to reach the excited state is approximately 3.8995 x 10^(-8) meters.
To calculate the wavelength of light required to move an electron from the ground state to the excited state in a hydrogen atom, you can use the formula
ΔE = hc/λ
Where:
ΔE is the change in energy between the two states (in this case, it is the energy of the excited state minus the energy of the ground state).
h is Planck's constant, approximately 6.63 × 10^(-34) joule-seconds.
c is the speed of light, approximately 3.00 × 10^8 meters per second.
λ is the wavelength of light.
Let's calculate it step by step:
1. Calculate the change in energy (ΔE):
ΔE = E_excited - E_ground
= (2.914 × 10^(-18) J)
= 2.914 × 10^(-18) J
2. Substitute the known values into the formula:
ΔE = hc/λ
We need to rearrange the formula to solve for λ:
λ = hc/ΔE
3. Substitute the values of the constants:
h = 6.63 × 10^(-34) J·s
c = 3.00 × 10^8 m/s
ΔE = 2.914 × 10^(-18) J
λ = (6.63 × 10^(-34) J·s) × (3.00 × 10^8 m/s) / (2.914 × 10^(-18) J)
4. Calculate the wavelength:
λ ≈ 6.80 × 10^(-7) meters
Therefore, the wavelength of light required to move a hydrogen atom from its ground state to an excited state with an energy of +2.914 × 10^(-18) J is approximately 6.80 × 10^(-7) meters (or 680 nm).