Using the Bohr’s model calculate the speed of the electron in ahydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbitalperiod in each of these levels

To calculate the speed of the electron in a hydrogen atom using Bohr's model, we can use the formula:

v = (Z * e^2) / (4 * π * ε₀ * n * ħ)

where:

• v is the speed of the electron
• Z is the atomic number (which is 1 for hydrogen)
• e is the elementary charge (1.602 x 10^-19 C)
• π is a mathematical constant (approximately 3.14159)
• ε₀ is the vacuum permittivity (8.854 x 10^-12 C^2 / N m^2)
• n is the principal quantum number (1, 2, or 3)
• ħ is the reduced Planck's constant (1.055 x 10^-34 J s)

Let's calculate the speed of the electron for each of the given levels:

For n = 1: v₁ = (1 * (1.602 x 10^-19 C)^2) / (4 * 3.14159 * 8.854 x 10^-12 C^2 / N m^2 * 1 * 1.055 x 10^-34 J s)

For n = 2: v₂ = (1 * (1.602 x 10^-19 C)^2) / (4 * 3.14159 * 8.854 x 10^-12 C^2 / N m^2 * 2 * 1.055 x 10^-34 J s)

For n = 3: v₃ = (1 * (1.602 x 10^-19 C)^2) / (4 * 3.14159 * 8.854 x 10^-12 C^2 / N m^2 * 3 * 1.055 x 10^-34 J s)

To calculate the orbital period in each of these levels, we can use the formula:

T = (2 * π * r) / v

where:

• T is the orbital period
• r is the radius of the orbit (which can be calculated using the Bohr radius formula: r = (0.529 x 10^-10 m) * n^2)
• v is the speed of the electron

Let's calculate the orbital period for each of the given levels:

For n = 1: r₁ = (0.529 x 10^-10 m) * 1^2 T₁ = (2 * 3.14159 * r₁) / v₁

For n = 2: r₂ = (0.529 x 10^-10 m) * 2^2 T₂ = (2 * 3.14159 * r₂) / v₂

For n = 3: r₃ = (0.529 x 10^-10 m) * 3^2 T₃ = (2 * 3.14159 * r₃) / v₃

By plugging in the values and performing the calculations, we can determine the speed of the electron and the orbital period for each of the given levels in the hydrogen atom.