**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.