These are two questions and two answers
Question 1.
Answer:
Explanation:
<u>1) Data:</u>
a) m = 9.11 × 10⁻³¹ kg
b) λ = 3.31 × 10⁻¹⁰ m
c) c = 3.00 10⁸ m/s
d) s = ?
<u>2) Formula:</u>
The wavelength (λ), the speed (s), and the mass (m) of the particles are reltated by the Einstein-Planck's equation:
- h is Planck's constant: h= 6.626×10⁻³⁴J.s
<u>3) Solution:</u>
Solve for s:
Substitute:
- s = 6.626×10⁻³⁴J.s / ( 9.11 × 10⁻³¹ kg × 3.31 × 10⁻¹⁰ m) = 2.20 × 10 ⁶ m/s
To express the speed relative to the speed of light, divide by c = 3.00 10⁸ m/s
- s = 2.20 × 10 ⁶ m/s / 3.00 10⁸ m/s = 7.33 × 10 ⁻³
Answer: s = 7.33 × 10 ⁻³ c
Question 2.
Answer:
Explanation:
<u>1) Data:</u>
a) m = 45.9 g (0.0459 kg)
b) s = 70.0 m/s
b) λ = ?
<u>2) Formula:</u>
Macroscopic matter follows the same Einstein-Planck's equation, but the wavelength is so small that cannot be detected:
- h is Planck's constant: h= 6.626×10⁻³⁴J.s
<u>3) Solution:</u>
Substitute:
- λ = 6.626×10⁻³⁴J.s / ( 0.0459 kg × 70.0 m/s) = 2.06 × 10 ⁻³⁴ m
As you see, that is tiny number and explains why the wave nature of the golf ball is undetectable.
Answer: 2.06 × 10 ⁻³⁴ m.
Answer:
0.6 grams of hydrogen are needed to react with 2.75 g of nitrogen.
Explanation:
When hydrogen and nitrogen react they form ammonia.
Chemical equation:
N₂ + 3H₂ → 2NH₃
Given mass of nitrogen = 2.75 g
Number of moles of nitrogen:
Number of moles = mass/ molar mass
Number of moles = 2.75 g / 28 g/mol
Number of moles = 0.098 mol
Now we will compare the moles of nitrogen with hydrogen from balance chemical equation:
N₂ : H₂
1 : 3
0.098 : 3×0.098 = 0.3 mol
Mass of hydrogen:
Mass = number of moles × molar mass
Mass = 0.3 mol × 2 g/mol
Mass = 0.6 g
<span>The initial mole fraction of the hydrogen gas is the same value as the nitrogen gas due to the fact neither material consumes the other. Because of this equal ratios where mixed initially, with the outcome in volume being the same.</span>
