Question

How many wavelengths of $K{{r}_{86}}$ are there in one metre?
(a)2348123.73
(b) 1553164.13
(c) 652189.63
(d) 1650763.73

Answer 1

The wavelength of a periodic wave is its spatial period, or the distance over which the wave's form repeats. It's the distance between two adjacent corresponding points of the same phase on the wave, such two adjacent crests, troughs, or zero crossings, and it's a feature of both travelling and standing waves, as well as other spatial wave patterns. The spatial frequency is the inverse of the wavelength. The Greek letter lambda ( $\lambda$ ) is often used to represent wavelength. Modulated waves, as well as the sinusoidal envelopes of modulated waves or waves generated by the interference of multiple sinusoids, are sometimes referred to as wavelengths.

Complete answer:
Krypton is an atomic number 36 chemical element with the symbol Kr. It is a colourless, odourless, and tasteless noble gas that is found in tiny amounts in the environment and is frequently employed in fluorescent lights alongside other rare gases. Krypton is chemically inert, with a few exceptions. Krypton has numerous distinct emission lines (spectral signatures), the strongest of which are green and yellow. One of the byproducts of uranium fission is krypton. The noble gas krypton has a face-centered cubic crystal structure, which is a feature shared by all noble gases (except helium, which has a hexagonal close-packed crystal structure).
Currently, the metre is defined as the length of light's journey in a vacuum in $\dfrac{1}{299\text{ }792\text{ }458}$ of a second.
Albert A. Michelson, the creator of the instrument and a proponent of adopting a certain wavelength of light as a standard of length, measured the standard metre for the first time with an interferometer in 1893. Interferometry was routinely used at the BIPM by 1925. However, until 1960, when the eleventh CGPM defined the metre in the new International System of Units (SI) as 1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum, the International Prototype Metre remained the norm.
Hence option (a) is correct.

Note:
The metre was first defined in 1793 as one ten-millionth of the distance in a great circle from the equator to the North Pole, implying that the Earth's circumference is roughly 40000 km. In 1799, a prototype metre bar was used to redefine the metre (the actual bar used was changed in 1889). The metre was redefined in 1960 in terms of a certain number of wavelengths of a krypton-86 emission line. The current definition was approved in 1983 and somewhat changed in 2002 to make it clear that the metre is a unit of appropriate length.