What is the speed of a particle of mass 10-27kg whose wavelength is 10-8m.
[h = 6.63 x 10-34Js]
6.63ms-1
66.30ms-1
663.00ms-1
6630.00ms-1
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From einstien's equation
E = ∆MV^2 m-mass -velocity
E is also E = hf = hV/λ
h=planks constant λ-wavelength hV/λ = mv^2
Solve accordingly and make v subject
V=h/mλ
=6.63x10^-34/10^-27x10^-8
=6.63x10^-34+27+8
=6.63x10^1
V=66.3
use the wave eqn ∆ =h/mv
where ∆ = wave length
h = Planck's constant
m= mass
v=velocity.(c, which is velocity of light can b used if asked)
What you're solving for The speed of a particle given its mass and wavelength. What's given in the problem Mass of the particle: \(m=10^{-27}\text{\ kg}\) Wavelength of the particle: \(\lambda =10^{-8}\text{\ m}\) Planck's constant: \(h=6.63\times 10^{-34}\text{\ Js}\) Helpful information De Broglie's wavelength formula: \(\lambda =\frac{h}{p}=\frac{h}{mv}\), where \(p\) is momentum and \(v\) is velocity. .f5cPye .WaaZC:first-of-type .rPeykc.uP58nb:first-child{font-size:var(--m3t3);line-height:var(--m3t4);font-weight:400 !important;letter-spacing:normal;margin:0 0 10px 0}.rPeykc.uP58nb{font-size:var(--m3t5);font-weight:500;letter-spacing:0;line-height:var(--m3t6);margin:20px 0 10px 0}.f5cPye ol{font-size:var(--m3t7);line-height:var(--m3t8);margin:10px 0 20px 0;padding-left:24px}.f5cPye .WaaZC:first-of-type ol:first-child{margin-top:0}.f5cPye ol.qh1nvc{font-size:var(--m3t7);line-height:var(--m3t8)}.PpKptb{color:var(--m3c11) !important;font-family:Google Sans,Roboto,sans-serif;font-size:var(--m3t11);font-weight:500;line-height:var(--m3t12)}.BFxDoe{color:var(--m3c10) !important;font-family:Google Sans,Roboto,sans-serif;font-size:var(--m3t9);letter-spacing:0.1px;line-height:var(--m3t10)}.UnzV3b{color:var(--m3c11);font-size:var(--m3t7);line-height:var(--m3t8)}.f5cPye ul .UrtGC,.f5cPye ol .UrtGC{margin-left:-24px}.UrtGC .dnXCYb[aria-expanded="true"] .WltAjf,.UrtGC .dnXCYb.yMbVTb .WltAjf{-webkit-line-clamp:unset}.UrtGC .dnXCYb{overflow:hidden}.UrtGC .dnXCYb{padding:0 !important}.UrtGC>.KLEmSd{margin:0 !important}.aj35ze{fill:#747878;display:inline-block;height:24px;width:24px}.h373nd{position:relative}.h373nd.HYvwY .dnXCYb{padding:0}.KcrKGb .IZE3Td,.KcrKGb .GKFAcc{padding:0 16px}.h373nd.HYvwY .ysxiae{margin:0}.dnXCYb{align-items:center;box-sizing:border-box;display:flex;min-height:48px;position:relative;width:100%;cursor:pointer}.dnXCYb{padding:0 16px}html:not(.zAoYTe) .dnXCYb{outline:0}.JlqpRe{flex:1;margin:12px 0;overflow:hidden}.h373nd:not(.LJm5W) .JCzEY{font-weight:500}.ABs8Y{font-weight:500}.ABs8Y,.JCzEY{color:var(--YLNNHc)}.APjcId,.WltAjf{color:var(--IXoxUe)}.WltAjf::before{content:'';display:block;height:4px}.bCOlv{width:100%}.bCOlv:not(.yMbVTb){position:absolute;display:none;opacity:0}.bCOlv:not(.yMbVTb) .GKFAcc{opacity:0}.IZE3Td{position:relative}.ru2Kjc{display:none}.L3Ezfd{position:absolute;height:100%;width:100%;left:0;top:0}.J2MhIb.LJm5W .JCzEY{font-weight:700}.ABs8Y,.JCzEY,.bJi8Dd,.APjcId,.WltAjf{display:-webkit-box;-webkit-box-orient:vertical;overflow:hidden}.JCzEY{-webkit-line-clamp:2}.yMbVTb.dnXCYb .aj35ze{transform:scale3d(1,-1,1)}.iXPZfd.dnXCYb .ABs8Y,.iXPZfd.dnXCYb .JCzEY{-webkit-line-clamp:unset !important;word-break:unset !important}.yMbVTb.dhks6d .APjcId,.yMbVTb.dhks6d .WltAjf{opacity:0.001;height:0}.APjcId,.WltAjf{-webkit-line-clamp:1}.CC4Ctb .JCzEY{-webkit-line-clamp:1;word-break:break-all}.LJm5W .CC4Ctb.dnXCYb{min-height:calc(40px + 2*12px)}.KLEmSd{border-bottom:1px solid #d2d2d2}.KLEmSd{margin:0px 16px}.KLEmSd.ym1pid{margin:0}.iwY1Mb{height:0;width:0;opacity:0;display:block}.fxvkXe,.p8Jhnd{width:36px;height:36px;background:#f1f3f4;border-radius:50%;display:flex;justify-content:center;align-items:center;flex-shrink:0;margin:0 0 0 12px}.dnXCYb:not(.FjLqqd):not(.CC4Ctb) .p8Jhnd{margin:12px 0 12px 12px} How to solve Use De Broglie's wavelength formula to solve for the velocity \(v\). Step 1 . Rearrange De Broglie's wavelength formula to solve for velocity \(\lambda =\frac{h}{mv}\) \(v=\frac{h}{m\lambda }\) Step 2 . Substitute the given values into the equation \(v=\frac{6.63\times 10^{-34}\text{\ Js}}{(10^{-27}\text{\ kg})(10^{-8}\text{\ m})}\) Step 3 . Calculate the velocity \(v=\frac{6.63\times 10^{-34}}{10^{-35}}\frac{\text{m}}{\text{s}}\) \(v=6.63\times 10^{1}\frac{\text{m}}{\text{s}}\) \(v=66.3\frac{\text{m}}{\text{s}}\)
