Chemistry · Structure Of Atom · NEET
The velocity is v_n = 2.188 x 10^6 x (Z/n) m/s. Here Z is the atomic number (the nuclear charge) and n is the orbit number (1, 2, 3...). The number 2.188 x 10^6 m/s is the speed of the electron in the FIRST orbit of hydrogen (Z=1, n=1). For any other case, just multiply this number by Z/n. This is the fastest way to get the answer in NEET.
It moves SLOWER in higher orbits. Because v is proportional to 1/n, when n increases the speed goes down. In the 1st orbit the electron is fastest; in the 2nd orbit it is half that speed; in the 3rd orbit it is one-third. Many students wrongly think a bigger, higher orbit means a faster electron. The opposite is true: farther orbit = slower electron.
Bohr said angular momentum is quantised: mvr = nh/2 pi. Also, the Coulomb force pulling the electron equals the centripetal force needed for the circle. Solving these two together gives v = 2 pi Z e^2 / (n h) in CGS, which comes out numerically to 2.188 x 10^6 (Z/n) m/s. You do NOT need to derive it in the exam - just remember the final formula and the Z/n rule.
For hydrogen the ground state is Z=1 and n=1, so v = 2.188 x 10^6 x (1/1) = 2.188 x 10^6 m/s (about 2.19 x 10^6 m/s). This is roughly 1/137 of the speed of light. That fraction 1/137 is called the fine-structure constant, and it is a nice fact to remember for tricky NEET options.
Since v is proportional to Z/n, a higher Z makes the electron faster. In the first orbit (n=1): H has Z=1, He+ has Z=2, Li2+ has Z=3. So the speeds are in the ratio 1 : 2 : 3. For example the electron in He+ (Z=2, n=1) moves twice as fast as in hydrogen's first orbit. Always check BOTH Z and n before comparing.
For the same atom Z is fixed, so v is proportional to 1/n. First orbit v1 is proportional to 1/1 and second orbit v2 is proportional to 1/2. So v1 : v2 = 2 : 1. The electron in the first orbit moves twice as fast as in the second orbit. This 2:1 type ratio is a very common NEET question shortcut.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is 2.188 x 10^6 m/s (about 2.19 x 10^6 m/s), which is nearly 1/137 of the speed of light.
v is proportional to Z/n. Velocity rises with nuclear charge Z and falls as orbit number n rises.
In a higher orbit the electron is farther from the nucleus, so the pull is weaker and it needs less speed to stay in a stable circle. Mathematically v is proportional to 1/n.
It works only for single-electron (hydrogen-like) species such as H, He+, Li2+, Be3+. For multi-electron atoms Bohr's model fails.
Radius grows as n^2/Z while velocity falls as Z/n. So as you go outward the orbit gets much bigger but the electron gets slower.
