1B.9: Trouble with exponents and units

[Julia Lindner 1I]

A lamp rated at 32 W emits violet light of wavelength 420 nm. How many photons of blue light can the lamp generate in 2.0 s? How many moles of photons are emitted in that time interval?

For this problem, I tried using v=C/λ to find the frequency, then multiply that by two seconds to get the number of photons, and the weird thing is that I got the number in the back of the book but the wrong exponent- 10^15 instead of 10^20. I also didn't use the given 32 W and the units don't seem to work out right. How do I do this problem to get the correct exponent and correct units? Also, as a side note, I seem to be getting wrong exponents a lot in problems about the photoelectric experiment, even when I get the right number. Any idea what I'm doing wrong?

[almaochoa2D]

It could most likely be that you're plugging in things wrong into your calculator or you aren't using parenthesis. Because I multiplied 2 by 32 to cancel out the seconds and got 64 J. You the use the E= hc/wavelength equation and plug in what is given. You should get 4.7x10^-19 J photons^-1. After that you divide 64 J by the energy you previously got and you'll get 1.4x10^20 photons. From there you divide the number of photons by avogadro's # and you'll get the answer.

[Cameron_Greenberg_3C]

I started the same way you did and found the frequency using v=c/wavelength. I then used this frequency in the E=hv equation, which showed the energy per photon to be 4.7x10^-19. The lamp gives off 32 J/s so in 2 seconds, it released 64 J of energy. Dividing the 64 J of total energy by the 4.7x10^-19 J of energy in each photon gives the number of photons, 1.4x10^20. Part b just requires a conversion to moles using Avogadro's number. Hope this helps

[George Ghaly 2L]

To solve this question, you must calculate the total amount of energy released (32W x 2s)=64J and then consider the energy released by one photon with a wavelength 420nm, then divide the total energy/the energy of one photon. This will result in the correct answer. Also consider the appropriate SI units (kg, m, J)