The radius of Bohr has the value:īy considering electrons in circular, quantized orbits, Bohr calculated the energy of an electron in the nth level of hydrogen as: Where n is a positive integer and r(1) is the smallest radius allowed for the hydrogen atom, also known as the Bohr’s radius. The equation gives the mathematical expression for the allowed value of the atomic radius. Only shells with the radius specified by the equation below were permitted, and electrons could not exist between these shells. Bohr proposed that electrons orbited the nucleus in fixed-radius orbits or shells. The assumption was that the structure of atoms could be quantized. The Bohr Model of the Hydrogen Atom proposed the planetary model first, but an assumption about electrons was later made. Prior to Bohr’s model of the hydrogen atom, scientists were baffled as to why atomic emission spectra were quantized. The equations, however, did not explain why the hydrogen atom emitted those specific wavelengths of light. The wavelengths of some emission lines could even be fitted to mathematical equations in the relatively simple case of the hydrogen atom. The emitted light can be refracted by a prism, resulting in spectra with a distinct striped appearance due to the emission of specific wavelengths of light. When an element or ion is heated by a flame or excited by an electric current, the excited atoms emit light of a specific color. As a result, mvr = nh/2π, where m = electron mass, v = electron tangential velocity, and r = radius of Bohr energy levels.Īnother example of quantization is atomic line spectra. This integral multiple is known as the hydrogen atom’s primary quantum energy level.
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