Question

The silicon–silicon single bond that forms the basis of the mythical silicon-based creature the Horta has a bond strength of 3.80 eV . What wavelength of photon would you need in a (mythical) phasor disintegration gun to destroy the Horta?

Short answer

The wavelength of photon needed in a phasor disintegration un to destroy the Horta is $3.27\times {10}^{-7}m$.

Step-by-step solution

Define the energy of a photon.

The energy of a photon is inversely proportional to the wavelength $\mathit{\lambda }$of photon and directly proportional to the frequency f of wave.

$$\begin{gathered} \mathit{E}\mathbf{=}\mathit{h}\mathit{f} \\ \mathit{E}\mathbf{=}\frac{\mathbf{h}\mathbf{c}}{\mathbf{\lambda }} \end{gathered}$$

Where, the value of Planck’s constant $\mathit{h}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{626}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{34}}\mathit{J}\mathbf{.}\mathit{s}$.

Determine the wavelength of the photon.

Given that the bond strength is 3.80 eV .

The wavelength of the photon is:

$$\begin{gathered} \lambda =\frac{hc}{E} \\ =\frac{\left(6.62\times {10}^{34}\right)\left(3.0\times {10}^8\right)}{\left(3.80\right)\left(1.60\times {10}^{-19}\right)} \\ =3.27\times {10}^{-7}m \end{gathered}$$

Hence, the wavelength of photon needed in a phasor disintegration un to destroy the Horta is $3.27\times {10}^{-7}m$.