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, we need to use the formula E = mv²/2, where E is the kinetic energy, m is the mass of the electron, and v is the velocity. In this case, we know that the radius of the electron's orbit is R = 5.3 • 10^-11 m. Using this, we can calculate the velocity of the electron using the formula v = 2πR/T, where T is the period of the electron's orbit. In the case of circular motion, the period is equal to the time for one full revolution, which is given by T = 2πR/v. Plugging this into the velocity formula, we get v = √(kme²)/h, where k is the Coulomb constant, me is the mass of the electron, and h is the Planck's constant. Now, to find the mass of the electron, we can use the formula me = 9.1094 • 10^-31 kg. Putting all these values into the kinetic energy formula, we get E = 0.51099891 • 10^-26 J. Multiplying this by 10^19, we get the answer of 510998.91 Nm. Since we are talking about very small values, it is often easier to express it in scientific notation, which gives us 5.1099891 x 10^23.
