You must have just punched in a wrong number.
E = (hc/wavelength)*6.02E23
E = (6.626E-34*3E8/2.88E-7)*6.02E23 in Joules.
Then divide by 1000 to convert to kJ and round to 3 places. I get 415.5 kJ which I would round to 416 kJ.
I got 4.16 * 10^8
but the correct answer is supposed to be 4.16 * 10^2.
E = (hc/wavelength)*6.02E23
E = (6.626E-34*3E8/2.88E-7)*6.02E23 in Joules.
Then divide by 1000 to convert to kJ and round to 3 places. I get 415.5 kJ which I would round to 416 kJ.
E = hc/λ
Where:
E is the energy in joules (J),
h is Planck's constant (6.62607015 × 10^-34 J·s),
c is the speed of light (2.998 × 10^8 m/s), and
λ is the wavelength of the photons in meters (m).
First, convert the given wavelength to meters:
2.88 × 10^-7 m
Next, substitute the values into the equation:
E = (6.62607015 × 10^-34 J·s)(2.998 × 10^8 m/s)/(2.88 × 10^-7 m)
Simplifying the expression gives:
E = 6.62607015 × 2.998 × 10^-34 × 10^8 /(2.88 × 10^-7)
E = 1.98876 × 10^-16 /(2.88 × 10^-7)
E ≈ 6.897642 × 10^-10 J
Now, convert the energy from joules to kilojoules by dividing by 1000:
6.897642 × 10^-10 J / 1000 = 6.897642 × 10^-13 kJ
To express this answer in scientific notation, we need to move the decimal point to the right, giving us:
6.897642 × 10^-13 = 6.897642 × 10^(-13-3) = 6.897642 × 10^-16 kJ/mol
Thus, the energy in kJ/mol for a mole of photons with a wavelength of 2.88 × 10^-7 m is approximately 6.897642 × 10^-16 kJ/mol.
Note: The answer you obtained, 4.16 × 10^8, is incorrect.