The hydrogen atom model and the Rydberg constant

Problem Statement

In Bohr's atomic model, the energy states of electrons orbiting the electrodes or nucleus are discontinuous (quantized) and are specified using the quantum number $n$n ($n=1, 2, 3, ...).

When a photon is shone onto an electron in a hydrogen atom in its ground state ($n=1$n=1), the electron ionizes to the highest energy state ($n=\infty$n=∞). If $E_{\infty}$E∞​ is the minimum energy required for ionization (ionization energy), then the ground state energy $E_1$E1​ is expressed as follows:

$$E_1 = -E_{\infty}$$E1​=−E∞​

Furthermore, the energy level $E_n$En​ of a hydrogen atom in the state of quantum number $n$n is expressed using the ground state energy $E_1$E1​ as follows:

$$E_n = \frac{E_1}{n^2}$$En​=n2E1​​

Now, the electron of this hydrogen atom has transitioned from an excited state with quantum number $n=4$n=4 to a state with quantum number $n=2$n=2. Find the energy $\Delta E$ΔE of the photon emitted as a result of this transition.

Constraints

• $E_{\infty} = 2.18 \times 10^{-18} \ \text{J}$E∞​=2.18×10−18 J

Input Format

When the calculated photon energy $\Delta E$ΔE is expressed in units of $\text{J}$J, the value can be expressed as $A \times 10^{-23}$A×10−23. Find the value of the coefficient $A$A in this case and input the natural number obtained without rounding.