CHEMISTRY COMMUNITY

I got the second part of this question incorrect, I am assuming because of an accident when inputting the numbers into my calculator.
I have re-done the problem below and just want to make sure I am on the right track.

Q6. Microwave ovens use microwave electromagnetic radiation to cause vibrations within the molecules in food causing it to heat it up. Microwave radiation has a frequency of about 3x10^9 Hz. Determine the energy, in J, and the wavelength, in nm, of a microwave.

E=hv
E=(6.62608x10^-34 J*s)(3x10^9 s^-1)
E=2x10^-24 J

=c/v (from c=v)
= (2.99792x10^8 m*s^-1)/(3x10^9 s^-1)x(1 nm)/10^-9 m)
=9.99306667x10^-7 nm
= 10x10^-7 nm

When I did this problem to find wavelength I used wavelength= ch/E instead.

I also used wavelength=hc/E, but the way you do it works too. With rounding the answer is 10 x 10^7 (positive exponent of 7, not negative, because there's 10^9 nanometers in one meter)

I initially used the derived equation λ=hc/E but I realized it was easier to just use λ=c/v because all the values are given to you, but yes you are on the right track

I also used both E=hv and wavelength= c/v and came up with the same answer but using wavelength= hc/E is quicker and would result in less calculator error.

I think this is most likely just a calculator error. You should get the same answer regardless of what equation you use.

In addition, I also used E=hv and wavelength=c/v and came up with the same answer. But also using wavelenght=hc/E can work as well.

Megan Potter 1G wrote:I also used wavelength=hc/E, but the way you do it works too. With rounding the answer is 10 x 10^7 (positive exponent of 7, not negative, because there's 10^9 nanometers in one meter)

If you don't mind explaining more, just so I can possibly understand, why would 10^9 nanometers in one meter make the answer positive?

Gabi Landes 1-H wrote:

Megan Potter 1G wrote:I also used wavelength=hc/E, but the way you do it works too. With rounding the answer is 10 x 10^7 (positive exponent of 7, not negative, because there's 10^9 nanometers in one meter)

If you don't mind explaining more, just so I can possibly understand, why would 10^9 nanometers in one meter make the answer positive?

Yes if possible could you explain? I am pretty sure 1 x 10^-9 m is 1 nm not positive 9

So if you solve the equation you get this:

Wavelength = {(6.626 x 10^-34)(2.998 x 10^8)}/(1.99 x 10^-24)
wavelength = .099821 meters

there are 10^9 nanometers in one meter (nanometers are smaller so it makes sense that there should be a ton of them to make one meter)

using dimensional analysis to convert:
.099821 meters x (10^9 nm)/1m = 9.982 x 10^7 nm as the wavelength

hope this helps! let me know if there's something else I can explain

Paywand Baghal wrote:

Gabi Landes 1-H wrote:

Megan Potter 1G wrote:I also used wavelength=hc/E, but the way you do it works too. With rounding the answer is 10 x 10^7 (positive exponent of 7, not negative, because there's 10^9 nanometers in one meter)

If you don't mind explaining more, just so I can possibly understand, why would 10^9 nanometers in one meter make the answer positive?

Yes if possible could you explain? I am pretty sure 1 x 10^-9 m is 1 nm not positive 9

see my explanation above but yes you are right, 1x10^-9 m = 1nm, so 1x10^9 nm=1 m :)