Question

1. isotopes vs. atomic mass

a. define isotope in your own words.
b. explain why the atomic mass on the periodic table is not a whole number.

1. quantitative isotope problem

boron exists naturally as two isotopes, b - 10 and b - 11.
isotope mass (amu) natural abundance
b - 10 10.013 19.78%
b - 11 11.009 80.22%

1. calculate the average atomic mass of boron, showing all work and using proper significant figures.

part iii: the nature of light (wave - particle duality)

1. light relationships

a. write the equation that relates wavelength, frequency, and the speed of light, and define each symbol.
b. describe the relationship between wavelength and frequency in words.

1. photon energy comparison

the energy of a 500 nm photon is 4.0×10⁻¹⁹j.
calculate the energy of a 250 nm photon and explain why the energy changes.

1. emission vs. absorption

which electronic transition in a hydrogen atom emits the most energy, and why?

• n = 4→n = 2
• n = 7→n = 3
• n = 2→n = 4
• n = 3→n = 7

Explanation:

Step1: Convert % to decimals

B-10: $19.78\% = 0.1978$; B-11: $80.22\% = 0.8022$

Step2: Calculate weighted mass for B-10

$\text{Weighted mass}_1 = 0.1978 \times 10.013 = 1.9806$

Step3: Calculate weighted mass for B-11

$\text{Weighted mass}_2 = 0.8022 \times 11.009 = 8.8314$

Step4: Sum weighted masses

$\text{Average mass} = 1.9806 + 8.8314 = 10.812$

Step5: Round to sig figs

Round to 4 significant figures: $10.81$

3a.

Isotopes are atoms of the same element (same proton count) that have different numbers of neutrons, so they have different atomic masses.

3b.

Atomic mass on the periodic table is a weighted average of the masses of an element's naturally occurring isotopes, accounting for their relative abundances, so it is rarely a whole number.

8a.

The equation is $c = \lambda f$, where:

• $c$ = speed of light in a vacuum ($3.00 \times 10^8$ m/s)
• $\lambda$ = wavelength of the light (distance per wave)
• $f$ = frequency of the light (waves per second)

8b.

Wavelength and frequency are inversely proportional: as wavelength increases, frequency decreases, and vice versa (since the speed of light is constant).

9.

Photon energy is inversely proportional to wavelength ($E = \frac{hc}{\lambda}$). A 250 nm photon is half the wavelength of a 500 nm photon, so its energy is double. Calculation: $E_2 = 2 \times 4.0 \times 10^{-19}\text{J} = 8.0 \times 10^{-19}\text{J}$. The energy increases because shorter wavelengths correspond to higher frequency, and higher frequency photons carry more energy.

10.

The transition $n=4 \to n=2$ emits the most energy. In hydrogen atoms, energy levels are closer together at higher $n$ values. The energy gap between $n=4$ and $n=2$ is larger than the gap between $n=7$ and $n=3$. The transitions $n=2 \to n=4$ and $n=3 \to n=7$ are absorption (not emission) transitions, so they do not emit energy.

Answer:

$10.81$ amu

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