## Conversions between meter/nanometers/picometers

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Lea 1F
Posts: 1
Joined: Fri Sep 25, 2015 3:00 am

### Conversions between meter/nanometers/picometers

Could someone please clarify for me the conversions between meters, nanometers, and picketers and when it is appropriate to use each?

Alex Nguyen 3I
Posts: 100
Joined: Fri Sep 25, 2015 3:00 am

### Re: Conversions between meter/nanometers/picometers

It's really easy to convert from the standard meters to another prefix and vice versa when the value is not in scientific notation. You just need to look at the chart in the course reader. There are $10^{-9}$ meters in a nanometer. So if you have 10, 20, or 30 meters, you would just say $10*10^{9}, 20*10^{9}$, and so on. Picometers is the same thing but to the power of 12. If you had nanometers or picometers, you would just use the negative value of that exponent (i.e. -9 or -12). However, when your answer is in scientific notation and you want to convert, you just need to remember to use conversion units. If you have $1.02*10^{-12}$ meters and you want to convert to nanometers, just figure out how many nanometers in a meter or how many meters in a nanometer. Since you want nanometers, keep the nanometers on the top. In this case, just multiply by $\frac{1*10^{9}nm}{1m}$. You could also multiply by $\frac{1nm}{1*10^{-9}m}$. As long as nm are on top. You'll always end up either subtracting or adding exponents. Once you get the hang of it, you can simply add or subtract exponents without writing out the actual conversion unit. Remember to move over the decimal place if need be at the end. As far as I know, velocity (m/s) and wavelength (m) requires specifically meters. Nanometers and picometers might be convenient to convert to at the end because some values for wavelengthon the EM radiation scale might be really small, but I don't know of any equations where they are required beforehand. Sorry this might sound confusing. Hope this helps though.