A Be3+ ion absorbs a photon with a frequency of 7.31 × 1015 Hz. If the energy of the final state of the Be3+ ion was -3.88 × 10(-18) J, calculate the energy of the initial state. Express answer in scientific notation.
My work so far:
delta E = (h)(v)
delta E = (6.63*10^34 Js)*(3.88*10^15)
delta E = 4.846 * 10^-18J
delta E = Ef - Ei
(4.846*10^-18) = 3.88*10^-18 - Ei
Ei = 9.66*10^-19J
Is this correct? I get confused with the negative signs in the energy values.
I think this is the same question which I've answered. If not, repost at the top of the page.
http://www.jiskha.com/display.cgi?id=1327912087
Your calculations are almost correct, but there seems to be a slight error in applying the negative sign. Let's go through the calculations step by step to clarify:
Given:
Frequency, v = 7.31 × 10^15 Hz
Energy of the final state, Ef = -3.88 × 10^-18 J
Step 1: Calculate the change in energy (delta E)
delta E = (h)(v), where h is the Plank's constant (6.63 × 10^-34 Js)
delta E = (6.63*10^-34 Js)(7.31*10^15 Hz)
delta E = 4.84 × 10^-18 J
Step 2: Calculate the energy of the initial state (Ei)
Since the initial state had a lower energy than the final state, the energy change is negative. Therefore, the equation becomes:
delta E = Ef - Ei
-4.84 × 10^-18 J = -3.88 × 10^-18 J - Ei
Now, you need to solve for Ei:
Ei = -4.84 × 10^-18 J + 3.88 × 10^-18 J
Ei = -9.6 × 10^-19 J
So, the energy of the initial state is -9.6 × 10^-19 J.
Therefore, your calculated value of the energy of the initial state is almost correct, but it should be -9.6 × 10^-19 J (rounded to two significant figures) instead of 9.66 × 10^-19 J.
Your calculations are almost correct. Let's go through them step by step:
1. You correctly used the formula delta E = (h)(v), where delta E represents the change in energy, h is Planck's constant (6.63 × 10^(-34) Js), and v is the frequency of the absorbed photon (7.31 × 10^15 Hz).
2. Plugging in the values: delta E = (6.63 × 10^(-34) Js) × (7.31 × 10^15 Hz).
3. Multiplying the numbers together gives: delta E = (6.63 × 7.31) × (10^(-34) × 10^15) = 48.3453 × 10^(-19) J.
However, you made a mistake in converting this answer to scientific notation. The correct scientific notation is 4.83453 × 10^(-18) J, not 4.846 × 10^(-18) J.
4. Now you correctly use the equation delta E = Ef - Ei, where Ef represents the energy of the final state (-3.88 × 10^(-18) J) and Ei represents the energy of the initial state (which we need to solve for).
5. Plugging in the values: (4.83453 × 10^(-18) J) = (-3.88 × 10^(-18) J) - Ei.
6. Rearranging the equation to solve for Ei gives: - Ei = (4.83453 × 10^(-18) J) - (-3.88 × 10^(-18) J),
or Ei = (-4.83453 + 3.88) × 10^(-18) J.
7. Simplifying the numbers gives: Ei = (-0.95453) × 10^(-18) J.
Thus, your final answer is Ei = -9.5453 × 10^(-19) J. The negative sign indicates that the initial state has lower energy than the final state.