What transition energy corresponds to an absorption line at 527 nm?
A. $2.65 x 10^{-19} J$
B. $5.69 x 10^{-19} J$
C. $3.77 x 10^{-19} J$
D. $3.26 x 10^{-19} J
Answer (2)
The transition energy corresponding to an absorption line at 527 nm is calculated using the formula E = λ h c , resulting in an energy of approximately 3.77 × 1 0 − 19 J . This matches option C. Therefore, the correct answer is C.
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Convert the wavelength from nanometers to meters: λ = 527 nm = 527 × 1 0 − 9 m .
Use the formula E = λ h c to calculate the energy.
Plug in the values: E = 527 × 1 0 − 9 m ( 6.626 × 1 0 − 34 J s ) × ( 3.0 × 1 0 8 m/s ) = 3.7719 × 1 0 − 19 J .
The transition energy is approximately 3.77 × 1 0 − 19 J .
Explanation
Understanding the Problem We are given an absorption line at a wavelength of 527 nm and asked to find the corresponding transition energy. To do this, we will use the formula that relates energy, Planck's constant, the speed of light, and wavelength: E = λ h c , where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.
Converting Wavelength to Meters First, we need to convert the wavelength from nanometers (nm) to meters (m). Since 1 nm = 1 0 − 9 m, we have: λ = 527 nm = 527 × 1 0 − 9 m .
Calculating the Energy Now, we can use the formula E = λ h c to calculate the energy. We know that Planck's constant h = 6.626 × 1 0 − 34 J s and the speed of light c = 3.0 × 1 0 8 m/s . Plugging in these values, we get: E = 527 × 1 0 − 9 m ( 6.626 × 1 0 − 34 J s ) × ( 3.0 × 1 0 8 m/s ) E = 527 × 1 0 − 9 m 1.9878 × 1 0 − 25 J m E = 3.7719 × 1 0 − 19 J .
Selecting the Correct Option Comparing our calculated energy value to the given options, we see that it is closest to option C, which is 3.77 × 1 0 − 19 J .
Final Answer Therefore, the transition energy corresponding to an absorption line at 527 nm is approximately 3.77 × 1 0 − 19 J .
Examples
Understanding the energy of light at different wavelengths is crucial in many real-world applications. For example, in solar panel technology, different materials are used to absorb light at different wavelengths to maximize energy conversion. Similarly, in medical imaging, specific wavelengths of light are used to visualize different tissues and structures within the body. The relationship between wavelength and energy also plays a vital role in understanding the colors we see, as each color corresponds to a specific range of wavelengths and energies.
