what frequency of radiation in Hz is required to ionise helium?
I would use the following:
1/wavelength = RZ^2(1/n1^2 - 1/n2^2)
R is the Rydberg constant = 1.097 x 10^7.
Z for He is 2 (and that is squared).
n1 = 1
n2 = infinity (which makes 1/n2^2=0).
Then convert wavelength (in meters) to frequency by using c = frequency x wavelength.
The ionization energy of helium is approximately 24.587 electron volts (eV), which is equivalent to 3.939 × 10^-18 joules. To calculate the frequency required to ionize helium, we can use the equation:
E = hf
where E is the energy of a photon, h is Planck's constant (6.626 × 10^-34 J·s), and f is the frequency of the radiation.
Rearranging the equation, we have:
f = E / h
Substituting the ionization energy of helium, we get:
f = (3.939 × 10^-18 J) / (6.626 × 10^-34 J·s)
Calculating this, we find:
f ≈ 5.96 × 10^15 Hz
Therefore, a frequency of approximately 5.96 × 10^15 Hz or 5.96 petahertz (PHz) is required to ionize helium.
To calculate the frequency of radiation needed to ionize helium, we can use the equation:
E = hf
where E is the energy required to ionize an atom, h is the Planck's constant (6.62607015 × 10^-34 J·s), and f is the frequency of the radiation.
The ionization energy of helium is approximately 24.6 eV (electron volts), which can be converted to joules using the conversion factor 1 eV = 1.602176634 × 10^-19 J.
So, the energy required to ionize helium in joules is:
E = 24.6 eV × 1.602176634 × 10^-19 J/eV
Now, we can rearrange the equation to solve for f:
f = E / h
Substituting the values, we get:
f = (24.6 eV × 1.602176634 × 10^-19 J/eV) / (6.62607015 × 10^-34 J·s)
Calculating this expression gives us the frequency in Hz required to ionize helium.