Multiple Choice
What is the wavelength necessary to completely remove an electron from the second shell (n = 2) of a hydrogen atom, given the Rydberg constant R∞ = 1.097 × 10^7 m^-1?
9. Quantum Mechanics
Wavelength and Frequency
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If one photon of light has 2.68 × 10⁻¹⁸ J of energy, it has a wavelength of _____________ nm. Use the formula E = hc/λ, where h = 6.626 × 10⁻³⁴ J·s and c = 3.00 × 10⁸ m/s.
A
74 nm
B
7400 nm
C
740 nm
D
74000 nm
Verified step by step guidance1
Start by identifying the formula given in the problem: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J·s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength.
Rearrange the formula to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).
Substitute the known values into the rearranged formula: \( \lambda = \frac{(6.626 \times 10^{-34} \text{ J·s})(3.00 \times 10^8 \text{ m/s})}{2.68 \times 10^{-18} \text{ J}} \).
Calculate the value of \( \lambda \) in meters. This involves performing the multiplication in the numerator and then dividing by the energy \( E \).
Convert the wavelength from meters to nanometers by multiplying the result by \( 1 \times 10^9 \) (since 1 meter = \( 1 \times 10^9 \) nanometers).
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