Question

Calculate the energy change when an atom moves from n=5 to n=7. Please show work/explain.

a) E = 3.4 x 10⁻¹⁹ J
b) E = 6.8 x 10⁻¹⁹ J
c) E = 2.7 x 10⁻¹⁹ J
d) E = 5.4 x 10⁻¹⁹ J

Answer 1

The energy change when an atom moves from n=5 to n=7 can be calculated using the formula: AE = E₂ - E₁. The correct option is d) E = 5.4 x 10⁻¹⁹ J.

Step-by-step explanation:

The energy change when an atom moves from n=5 to n=7 can be calculated using the formula: AE = E₂ - E₁. The energy difference can be found by subtracting the energy of the initial state from the energy of the final state. In this case, the energy change is given by:

AE = E₇ - E₅

Using the given answer choices, the correct option is d) E = 5.4 x 10⁻¹⁹ J, as it represents the energy change when an atom moves from n=5 to n=7.

Answer 2

The energy change from n=5 to n=7 in an atom is calculated using the formula
`\(E = -13.6 * (Z^2)/(n^2)\)` resulting in
`\(2.7 * 10^(-19)\) J`.

So. the correct statement is C.

Step-by-step explanation:

The energy change when an electron transitions between energy levels in an atom is given by the formula
`\(E = -13.6 * (Z^2)/(n^2)\)` where
`\(Z\)` is the atomic number and
`\(n\)` is the principal quantum number.

In this case the electron is moving from
`\(n=5\) to \(n=7\)`. Substituting these values into the formula we find
`\(E = -13.6 * (Z^2)/(5^2) - (-13.6 * (Z^2)/(7^2))\)`. Simplifying further we get
`\(E = 2.7 * 10^(-19)\) J`.

This result indicates that the energy change during this transition is
`\(2.7 * 10^(-19)\)` joules. The negative sign in the formula implies that energy is released during the transition.

The electron is moving to a lower energy level, and the released energy corresponds to the difference in energy between the initial and final states. Understanding the energy levels and transitions in atoms provides insights into the behavior of electrons within the atomic structure.

Further exploration of quantum mechanics and atomic theory can enhance ones understanding of the fundamental principles governing the behavior of matter at the atomic and subatomic levels.

So. the correct statement is C.