{"id":12287,"date":"2023-03-01T08:56:52","date_gmt":"2023-03-01T08:56:52","guid":{"rendered":"https:\/\/www.greatassignmenthelp.com\/questions\/?p=12287"},"modified":"2023-12-21T05:44:26","modified_gmt":"2023-12-21T05:44:26","slug":"a-monochromatic-laser-is-exciting-hydrogen-atoms-from-the-n2-state-to-the-n5-state","status":"publish","type":"post","link":"https:\/\/www.greatassignmenthelp.com\/questions\/a-monochromatic-laser-is-exciting-hydrogen-atoms-from-the-n2-state-to-the-n5-state\/","title":{"rendered":"A monochromatic laser is exciting Hydrogen atoms from the n=2 state to the n=5 state."},"content":{"rendered":"

A) What is the wavelength \u03bb of the laser? Express your answer to three significant digits in nanometers.<\/p>\n

(B) Eventually, all of the excited hydrogen atoms will emit photons until they fall back to the ground state. How many different wavelengths can be observed in this process?<\/p>\n

(C) What is the longest wavelength \u03bb_max that is observed? Express your answer to three significant digits in nanometers.<\/p>\n

(D) What is the shortest wavelength \u03bb_min observed? Express your answer to three significant digits in nanometers.<\/p>\n

Answer:-\u00a0<\/strong>The energy of the laser must be higher than or equal to the energy of the transition of the hydrogen atom, whose levels of energy are defined by the Bohr model, in order to carry out this excitation.<\/p>\n

En = -13,606 \/ n\u00b2 [eV]<\/p>\n

as a result, the transition’s energy is<\/p>\n

\u0394E = E\u2085 -E\u2082<\/p>\n

\u0394E = 13.606 (1 \/ n\u2082\u00b2 – 1 \/ n\u2085\u00b2)<\/p>\n

\u0394E = 13.606 (1\/2\u00b2 – 1\/5\u00b2)<\/p>\n

\u0394E = 2,85726 eV<\/p>\n

Let’s apply Planck’s equation immediately.<\/p>\n

E = h f describes how wavelength and frequencies affect the speed of light.<\/p>\n

c = \u03bb f<\/p>\n

f = c \/\u03bb<\/p>\n

E = h c \/\u03bb<\/p>\n

\u03bb = h c \/ E<\/p>\n

Bring the energy down to the SI system.<\/p>\n

E = 1.6 1019 J \/ 1 eV \/ 2,85726 eV = 4.5716 1019 J<\/p>\n

Let’s compute.<\/p>\n

\u03bb = 6,626 10\u207b\u00b3\u2074 3 10\u2078 \/ 4,5716 10\u207b\u00b9\u2079<\/p>\n

\u03bb = 4.348 10\u207a\u2077 m (10\u2079 nm \/ 1 m)<\/p>\n

From this state with n = 5 to the base state n = 1, photon emission processes at = 435 nm can produce the transitional starting state n = 5.<\/p>\n

final condition n = 4<\/p>\n

\u0394E = 13.606 (1\/4\u00b2 – 1\/5\u00b2)<\/p>\n

\u0394E = 0.306 eV<\/p>\n

\u03bb = h c \/ E<\/p>\n

\u03bb = 4052 nm<\/p>\n

n = 5<\/p>\n

the final energy (E) (nm)<\/p>\n

level<\/p>\n

4 0.306 4052<\/p>\n

3 0.9675 1281<\/p>\n

2 2,857 435<\/p>\n

1 13.06 95<\/p>\n

n = 4<\/p>\n

3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.661\u00a0\u00a0\u00a0\u00a0\u00a0 1876<\/p>\n

2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2,551\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 486<\/p>\n

1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 11,905\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 104<\/p>\n

n = 3<\/p>\n

2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.89\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 656<\/p>\n

1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12.09\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 102.5<\/p>\n

n = 2<\/p>\n

1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10.20\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 121.6<\/p>\n

    \n
  1. c) \u03bb = 4052 nm<\/li>\n
  2. d) \u03bb= 95 nm<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    A) What is the wavelength \u03bb of the laser? Express your answer to three significant digits in nanometers. (B) Eventually, all of the excited hydrogen […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27],"tags":[],"yoast_head":"\nA monochromatic laser is exciting Hydrogen atoms from the n=2 state to the n=5 state.<\/title>\n<meta name=\"description\" content=\"A monochromatic laser is exciting Hydrogen atoms from the n=2 state to the n=5 state.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.greatassignmenthelp.com\/questions\/a-monochromatic-laser-is-exciting-hydrogen-atoms-from-the-n2-state-to-the-n5-state\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A monochromatic laser is exciting Hydrogen atoms from the n=2 state to the n=5 state.\" \/>\n<meta property=\"og:description\" content=\"A monochromatic laser is exciting Hydrogen atoms from the n=2 state to the n=5 state.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.greatassignmenthelp.com\/questions\/a-monochromatic-laser-is-exciting-hydrogen-atoms-from-the-n2-state-to-the-n5-state\/\" \/>\n<meta property=\"og:site_name\" content=\"Questions - 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