Problem:
What wavelength photon would be required to ionize a hydrogen atom in the ground state and give the ejected electron a kinetic energy of 19.1 eV ?
Answer--> λ =______nm
[Note: I got 3.8x10^-8. I got it wrong twice]
My steps:
(32.7 eV)(1.6x10^19)= 52.32x10^-19
Next I did this:
((6.626x10^-34)(3x10^8m/s))/(52.32x10^-19)=3.8x10^-8
My answer--> 3.8⋅10^−8
the answer is asking for nanometers
units?
Yes Sir
To find the wavelength of the photon required to ionize a hydrogen atom and give the ejected electron a kinetic energy of 19.1 eV, you need to use the equation:
E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J∙s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the photon.
First, convert the kinetic energy from eV to joules by using the conversion factor:
1 eV = 1.6 x 10^-19 J
19.1 eV = 19.1 x 1.6 x 10^-19 J = 30.56 x 10^-19 J
Now, rearrange the equation to solve for λ:
λ = hc/E
Substitute the values into the equation:
λ = (6.626 x 10^-34 J∙s) x (3 x 10^8 m/s) / (30.56 x 10^-19 J)
Calculating this expression will give you the wavelength in meters. However, your answer should be in nanometers, so you need to convert it.
1 nm = 10^-9 m
Converting the wavelength from meters to nanometers:
λ_nm = λ x 10^9 nm
Now, follow these steps to find the accurate answer:
1. Calculate (6.626 x 10^-34 J∙s) x (3 x 10^8 m/s) to get the numerator.
2. Divide the numerator by (30.56 x 10^-19 J) to get the wavelength in meters.
3. Multiply the wavelength in meters by 10^9 to convert it to nanometers.
By following these steps, you will find the correct value for the wavelength (λ) in nanometers.