Question

question 19 this energy diagram shows the allowed energy levels of an electron in a certain atom or molecule: energy e d c the ground state is. the number of lines in absorption spectrum are with the longest wavelength for transition and the shortest wavelength for transition

Explanation:

Step1: Recall energy - wavelength relationship

The energy of a photon is given by $E = h
u=\frac{hc}{\lambda}$, where $h$ is Planck's constant, $
u$ is the frequency, $c$ is the speed of light and $\lambda$ is the wavelength. So, $\lambda=\frac{hc}{E}$, which means that longer - wavelength corresponds to lower energy and shorter - wavelength corresponds to higher energy.

Step2: Identify ground state

The ground state is the lowest - energy level. In the given energy - level diagram, the ground state is the lowest line, which is level E.

Step3: Calculate number of absorption lines

The number of absorption lines in an energy - level diagram with $n$ levels is given by the formula $\frac{n(n - 1)}{2}$. Here, $n=4$. So, $\frac{4\times(4 - 1)}{2}=\frac{4\times3}{2}=6$.

Step4: Find longest - wavelength transition

The longest - wavelength transition corresponds to the smallest energy difference. The smallest energy difference occurs between adjacent levels. The transition from E to D has the smallest energy difference, so it has the longest wavelength.

Step5: Find shortest - wavelength transition

The shortest - wavelength transition corresponds to the largest energy difference. The largest energy difference occurs between the ground state (E) and the highest - energy level (C). So, the transition from E to C has the shortest wavelength.

Answer:

Ground state: E
Number of lines in absorption spectrum: 6
Longest - wavelength transition: E to D
Shortest - wavelength transition: E to C