[Hemidol]

An atom of some element X has three electronic transitions, A, B, and C. Suppose that it has been
found that the wavelength for transition A is 419.2 nm and that for B is 596.2 nm. (a) What is the energy (in
J) for a photon given off in transition C? (b) What is the wavelength (in nm) for transition C?

Here is the diagram: http://209.85.12.227/1318/19/upload/p10694844.jpg


Here is my work...

(a) E = h * speed of light / wavelength

nm conversion -> 1015.4nm * (1 * 10^-9m / 1nm) = 1.0154 * 10^-6m

E = (6.6256 * 10^-34 J-sec) * (2.9979 * 10⁸ m/s / 1.0154 * 10^-6m) = 1.956163703 * 10^-19 J


(b) Simply add the wavelengths of A + B to yield 1015.4nm.


Is this correct problem solving? I have a feeling b is incorrect due to the direction of energy, what does this signify?

[Borek]

You can't add wavelengths, you can add energies. Check that it yields different results.

[Hemidol]

You can't add wavelengths, you can add energies. Check that it yields different results.

Ah thank you much Borek. I wasn't aware at all that you can't add wavelengths. This is so fundamental, yet I missed it.


So I shall rework this problem as such calculating the enerigies of all arrows:

Arrow A Energy Calculations:

Step 1: Nanometer conversions -> 419.2 nm * (1 * 10^-9m / 1nm) = 4.192 * 10^-7m

Step 2:
Energy calculation of arrow A:
E = h * speed of light / wavelength

= (6.6256 * 10^-34 J-sec) * (2.9979 * 10⁸ m/s / 4.192 * 10^-7m) = 4.73828 * 10^-19


Arrow B Energy Calculations:

Step 1: Nanometer conversions -> 596.2 nm * (1 * 10^-9m / 1nm) = 5.962 * 10^-7m

Step 2:
Energy calculation of arrow A:
E = h * speed of light / wavelength

= (6.6256 * 10^-34 J-sec) * (2.9979 * 10⁸ m/s / 5.962 * 10^-7m) = 3.331581053 * 10^-19


Arrow C Energy Calculations:
3.331581053 * 10^-19 J + 4.73828 * 10^-19 J = 8.069861053 * 10^-19 J




For (b)


w = h * (c/e)
= (6.6256 * 10^-34 J-sec) * (2.9979 * 10⁸ m/s / 8.069861053 * 10^-19 J) = 2.461366572 * 10^-7 m

convert to nm: 2.461366572 * 10^-7 m / 1 * 10^-9 = 2.461366572 * 10^-16 nm



Are these better (correct)?

[Borek]

I think you got it wrong - we will be not checking your homework. Approach seems to be correct, no idea about intermediate numbers. They seem reasonable.

Final result is wrong for sure. Incorrect ballpark. You are adding energies of photons in the nm range, answer should be in the same range, not 10¹⁶ times smaller.

[Hemidol]

I think you got it wrong - we will be not checking your homework. Approach seems to be correct, no idea about intermediate numbers. They seem reasonable.

Final result is wrong for sure. Incorrect ballpark. You are adding energies of photons in the nm range, answer should be in the same range, not 10¹⁶ times smaller.

This isn't homework. This is me trying to learn chemistry on my own.


I'll try again and reply back later. 

[Hemidol]

I'm sorry to say it, but I believe all these equations are correct. 

[Yggdrasil]

convert to nm: 2.461366572 * 10^-7 m / 1 * 10^-9 = 2.461366572 * 10^-16 nm

Here's your problem.  The correct conversion is:

[Geddoe]

convert to nm: 2.461366572 * 10^-7 m / 1 * 10^-9 = 2.461366572 * 10^-16 nm

Here's your problem.  The correct conversion is:

Why did you use to the exponent 9 and not -9 there? Conceptually this answer does not correspond to the graph as in the graph C is longer then both A and B.

[Yggdrasil]

Why did you use to the exponent 9 and not -9 there?

10⁹nm = 1 m

Conceptually this answer does not correspond to the graph as in the graph C is longer then both A and B.

The wavelength of light is inversely proportional to its energy.