One of the lines in the spectrum of a mercury vapor lamp has a wave length of 254nm. What is the energy, in kj/mol, of this electro magnetic radiation.
The work I have done:
(6.626 x 10^-34 x 3.0 x 10^8) all divided by (254 x 10^-9.)
The answer I calculated is 7.82 x 10^-19. The actual answer is 471 Kj/mol.
Can someone please explain to me where I have gone wrong?
You just didn't go far enough. What you have is correct and the answer of 7.82 x 10^-19 joules is the energy PER PHOTON. The question asks for kJ/mol; therefore, multiply your answer by 6.022 x 10^23 to convert to moles, then divide by 1000 to convert to kJ/mol. I obtain 471.
Thank you very much.
To find the energy of electromagnetic radiation, you need to use the formula:
E = hc / λ
where E is the energy, 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.
In your calculation, you correctly multiplied Planck's constant (h) by the speed of light (c), but then you divided it by the wavelength (λ) in meters instead of converting the wavelength from nanometers to meters.
To calculate the energy correctly, you need to convert the wavelength from nanometers to meters before plugging it into the formula. Remember that 1 meter is equal to 10^9 nanometers.
Let's redo the calculation:
Given:
Wavelength (λ) = 254 nm = 254 x 10^-9 m
h = 6.626 x 10^-34 J·s
c = 3.0 x 10^8 m/s
Substituting the values into the formula:
E = (6.626 x 10^-34 J·s) x (3.0 x 10^8 m/s) / (254 x 10^-9 m)
Simplifying the expression:
E = 7.82 x 10^-19 J
To convert the energy to kilojoules per mole, you need to divide it by Avogadro's number (6.022 x 10^23). This conversion allows you to determine the energy per mole of photons:
E (in KJ/mol) = (7.82 x 10^-19 J) / (6.022 x 10^23) * (1 KJ / 10^3 J)
E = 471 KJ/mol (rounded to three significant figures)
Therefore, the correct energy is indeed 471 KJ/mol, as you mentioned.