Final answer:
To find the radius of a hydrogen atom for an electron moving at a given speed, we reference the Bohr model's quantized orbit formulas and the relationship between centripetal force and electrostatic attraction, using constants like the Bohr radius.
Step-by-step explanation:
The student's question asks about the radius of a hydrogen atom when an electron within it moves at a specified speed. To determine this radius using the Bohr model of the hydrogen atom, we must refer to the Bohr radius and the principles of quantized orbits. The Bohr model states that the electrons move in circular orbits around the nucleus with certain allowed radii, which are determined by the energy level or quantum number n. The radius of the n-th orbit (rn) is given by rn = n2 × a0, where a0 is the Bohr radius (a0 = 5.292 × 10-11 m). Since the given electron speed is different from that of an electron in the ground state, the energy level n would also be different. However, to find the exact radius for the given speed, we need to apply principles that include the centripetal force acting on the electron due to electrostatic attraction, which is equal to the electron's mass multiplied by the velocity squared, divided by the radius. The relevant formula to relate the given speed to the Bohr model and find the new radius is more complex and would typically be covered in a physics course at an advanced high school or college level.