In the Bohr model of a hydrogen atom, an electron orbits a proton at a distance
ID: 1906843 • Letter: I
Question
In the Bohr model of a hydrogen atom, an electron orbits a proton at a distance of R = 5.3 . 10-11 m. Since an accelerating charge generates electromagnetic radiation, the Bohr atom is not stable. The electron radiates its energy away and spirals into the nucleus. What is the initial rate of energy loss? If the rate of energy loss were constant, how long would it take an electron to radiate away all of its kinetic energy?Explanation / Answer
The phenomenon of spontaneous emission of highly penetrating and ionizing radiations by unstable and usually heavy nucleus is called radioactivity. it is spontaneous and is unaffected by external agents like temperature, pressure, electric and magnetic field etc. Average Life / Mean Life of a radioactive substance is defined as the ratio of total life time of all the radioactive atoms to the total number of atoms in it. Half life period of a radioactive element is defined as the time taken for one half of the radio active element to undergo disintegration. Derivation From the law of disintegration N = No e^(-?t) ------> eq(1) Where N is the number of nucleus preset at that instant 't' , No is the number of nucleus present initially and ? is the decay constant / disintegration constant So when instant t = T½ ---> Half life Period N = No/2 eq(1) ===> No/2 = No e^(-?.T½) 1/2 = e^(-?.T½) reciprocal on both sides 2 = e^(?.T½) ln 2 = ?.T½ ---- (ln 2 => log of 2 to the base 'e' ) T½ = 0.6931/? This is the equation for half life period