Question

Transition A produces light with a wavelength of 470 nm. Transition B involves twice as much energy as A. What wavelength light does it produce?

Answer 1

Transition A produces light with a wavelength of $470\mathrm{nm}$. Transition B involves twice as much energy as A. What wavelength light does it produce?

Solution

We have the $\varepsilon = h\nu$ ($\varepsilon$ is energy of one photon, $h$ is Planck constant), $\nu = \frac{c}{\lambda}$, $\lambda$ is wavelength, $\nu$ is frequency, $c$ is speed of light.

If transition A produces

$$\varepsilon_{A} = h \frac{c}{\lambda_{A}}$$

And transition B involves

$$\varepsilon_{B} = 2 \varepsilon_{A}$$ $$\varepsilon_{B} = h \frac{c}{\lambda_{B}}$$

From here we have wavelength of transition B

$$\lambda_{B} = \frac{\lambda_{A}}{2} = 235\mathrm{nm}$$