Find wavelength of a quantum of electromagnetic radiation

[trivk96]

Homework Statement

A quantum of electromagnetic radiation has
an energy of 0.877 keV.
What is its wavelength? The speed of light
is 2.99792 × 10
8 m/s, and Planck’s constant
is 6.62607 × 10−34J · s.
Answer in units of nm

Homework Equations

E=hf
v=fλ
... λ=v/(E/h)

The Attempt at a Solution

When i solved, i got 1.413728e-9 nm... I have checked my units. can some just help and point me in the right direction

 

[Dickfore]

v is usually written as c when one speaks of the speed of light in vacuum. Also, the double fraction reduces to:
$$\frac{c}{\frac{E}{h}} = \frac{h \, c}{E}$$
For this answer, you need to know the conversion factor between an electron-volt (eV) and a joule as energy units. Do you know it?

 

[trivk96]

v is usually written as c when one speaks of the speed of light in vacuum. Also, the double fraction reduces to:
$$\frac{c}{\frac{E}{h}} = \frac{h \, c}{E}$$
For this answer, you need to know the conversion factor between an electron-volt (eV) and a joule as energy units. Do you know it?

Yes i did convert it but i still got it wrong

 

[Dickfore]

how did you convert it, and what did you get?

 

[trivk96]

I did it again and i got 1.414E-8 ... and i think that is in meters. Am i right??

so that means that the answer is14.14nm
________________________________________________________________________

I used Plancks constant in eV's. Its on the ap equation sheet

 

[Dickfore]

I didn't get that. What did you get for the energy in joules?

 

[trivk96]

1.405109518e-16 J

 

[Dickfore]

This is correct. Now:
$$\frac{h \, c}{E} = \frac{6.626 \times 10^{-34} \, \mathrm{J} \cdot \mathrm{s} \times 2.998 \times 10^8 \, \mathrm{m} \cdot \mathrm{s}^{-1}}{1.4051 \times 10^{-16} \, \mathrm{J}}$$

The product and ratio of the mantissas, gives:
$$\frac{6.626 \times 2.998}{1.4051} = 14.14$$
The exponents sum up to $-34 + 8 - (-16) = -10$. You may read off the units from the above fraction fairly easily.

What should the answer be in scientific form?

 

[trivk96]

so in nm, it would be 1.414

 

[Dickfore]

yes, except that you need to use as many significant figures, as there are in variable with the least number of significant figures given in the problem. Fundamental constants are usually known to a lot of significant figures.

 

[trivk96]

Thank You