Can someone please help me with the numerical of chemistry part 1 text...
Can someone please help me with the numerical of chemistry part 1 text...
**Problem 2.10:**
The problem states: "If the velocity of the electron in Bohr's first orbit is 2.19 x 10^6 m/s, calculate the de Broglie wavelength associated with it."
To find the de Broglie wavelength associated with an electron in Bohr's first orbit, we can use the de Broglie equation:
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the electron.
Step 1: Find the momentum of the electron.
The momentum of an electron can be calculated using the equation:
p = m * v
Where p is the momentum, m is the mass of the electron (9.11 x 10^-31 kg), and v is the velocity of the electron.
p = (9.11 x 10^-31 kg) * (2.19 x 10^6 m/s)
p ≈ 1.99 x 10^-24 kg·m/s
Step 2: Calculate the de Broglie wavelength.
Using the de Broglie equation:
λ = (6.626 x 10^-34 J·s) / (1.99 x 10^-24 kg·m/s)
λ ≈ 3.33 x 10^-10 m
Therefore, the de Broglie wavelength associated with the electron in Bohr's first orbit is approximately 3.33 x 10^-10 m.
**Problem 2.11:**
The problem states: "Calculate the wavelength of an electron moving with a velocity of 2.05 x 10^7 m/s."
To find the wavelength of an electron with a given velocity, we can use the de Broglie equation:
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the electron.
Step 1: Find the momentum of the electron.
The momentum of an electron can be calculated using the equation:
p = m * v
Where p is the momentum, m is the mass of the electron (9.11 x 10^-31 kg), and v is the velocity of the electron.
p = (9.11 x 10^-31 kg) * (2.05 x 10^7 m/s)
p ≈ 1.87 x 10^-23 kg·m/s
Step 2: Calculate the de Broglie wavelength.
Using the de Broglie equation:
λ = (6.626 x 10^-34 J·s) / (1.87 x 10^-23 kg·m/s)
λ ≈ 3.54 x 10^-12 m
Therefore, the wavelength of the electron moving with a velocity of 2.05 x 10^7 m/s is approximately 3.54 x 10^-12 m.
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