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structure of atom 47 Where m is the mass of electron, v is the e Niels Bohr velocity and r is the radius of the orbit in (1885–1962) which electron is moving. Niels Bohr, a Danish physicist Thus an electron can move only in those received his Ph.D. from the orbits for which its angular momentum is University of Copenhagen in integral multiple of h/2π. That means angular 1911. He then spent a year momentum is quantised. Radiation is emitted with J.J. Thomson and Ernest Rutherford in England. In 1913, or obsorbed only when transition of electron takes place from one quantised value of he returned to Copenhagen where he remained for angular momentum to another. Therefore, the rest of his life. In 1920 he was named Director Maxwell’s electromagnetic theory does not of the Institute of theoretical Physics. After first World War, Bohr worked energetically for peaceful apply here that is why only certain fixed orbits uses of atomic energy. He received the first Atoms are allowed. for Peace award in 1957. Bohr was awarded the The details regarding the derivation of Nobel Prize in Physics in 1922. energies of the stationary states used by Bohr, are quite complicated and will be discussed in Fig. 2.11 depicts the energies of different higher classes. However, according to Bohr’s theory for hydrogen atom: stationary states or energy levels of hydrogen a) The stationary states for electron are atom. This representation is called an energy numbered n = 1,2,3.......... These integral level diagram. numbers (Section 2.6.2) are known as Whentheelectronisfreefromtheinfluence Principal quantum numbers. of nucleus, the energy is taken as zero. The electron in this situation is associated with the b) The radii of the stationary states are expressed as: stationary state of Principal Quantum number r = n a (2.12) = n = ∞ and is called as ionized hydrogen atom. n 0 When the electron is attracted by the nucleus where a 0 = 52.9 pm. Thus the radius of and is present in orbit n, the energy is emitted the first stationary state, called the Bohr and its energy is lowered. That is the reason orbit, is 52.9 pm. Normally the electron in the hydrogen atom is found in this orbit (that is n=1). As n increases the What does the negative electronic energy (E n for hydrogen atom mean? value of r will increase. In other words the electron will be present away from The energy of the electron in a hydrogen the nucleus. atom has a negative sign for all possible orbits (eq. 2.13). What does this negative c) The most important property associated with the electron, is the energy of its sign convey? This negative sign means stationary state. It is given by the that the energy of the electron in the atom is lower than the energy of a free expression. electron at rest. A free electron at rest ▯ 1 ▯ is an electron that is infinitely far away E n ▯ R H 2 n = 1,2,3.... (2.13) ▯n ▯ from the nucleus and is assigned the where R is called Rydberg constant and energy value of zero. Mathematically, this H –18 corresponds to setting n equal to infinity its value is 2.18×10 J. The energy of the in the equation (2.13) so that ∞=0. As the lowest state, also called as the ground state, is electron gets closer to the nucleus (as n 1 E 1 –2.18×10 –18( 2 ) = –2.18×10 –18J. The decreases), E necomes larger in absolute 1 value and more and more negative. The energy of the stationary state for n = 2, will most negative energy value is given by n=1 which corresponds to the most stable be : E = –2.18×10 J (18 1 ) = –0.545×10 –18 orbit. We call this the ground state. 2 22 J. Reprint 2026-27