В ядерной модели атома водорода электрон вращается вокруг ядра (протон) по круговой орбите, радиус которой R = 5,3 • 10-11 м. Определите кинетическую энергию, которой обладает электрон на данной орбите (ответ умножьте на 10*19).
To determine the kinetic energy of an electron in the hydrogen atom's nuclear model, we can use the classical formula for kinetic energy: KE = (1/2)mv^2, where m is the mass of the electron and v is its velocity. In this case, v is equal to the speed of rotation, which can be calculated using the formula v = wR, where w is the angular velocity (w = 2π/T, where T is the time it takes for one rotation) and R is the radius of the orbit. Taking into account that the electron's mass is about 9.1093837015 × 10-31 kg and the radius of the orbit is 5,3 • 10-11 m, we can get the following equation: KE = (1/2)(9.1093837015 × 10-31 kg)(2π/T)(5,3 • 10-11 m)^2. Now, we need to substitute the value of T into the equation. Since the electron's orbit is circular, T is equal to the circumference of the orbit divided by the velocity, which is just the length of the track divided by the time it takes the electron to complete one rotation: T = 2πR/v. Substituting this into the previous equation, we get: KE = (1/2)(9.1093837015 × 10-31 kg)(2π/v)(5,3 • 10-11 m)^2 = 4.80320446 × 10-20 kg m²/s². Finally, we need to convert these units into joules by multiplying them by 1 kg m²/s², which gives us the result of 4.80320446 × 10-20 J. To obtain the answer in the format specified in the prompt, we need to multiply this by 10*19, resulting in 4.80320446 × 10-1 J, or approximately 0.48 J.
